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Common Core: 6th Grade Math : Ratios & Proportional Relationships

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Example Questions

Example Question #71 : Ratios & Proportional Relationships

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 800 $\displaystyle 800$ cars in the parking lot and $80\%$ $\displaystyle 80\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

460 $\displaystyle 460$

$\displaystyle 80$

630 $\displaystyle 630$

640 $\displaystyle 640$

360 $\displaystyle 360$

Correct answer:

640 $\displaystyle 640$

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $80\%$ $\displaystyle 80\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 80$ of them are red. We can write the following ratio:

$80:100\rightarrow\frac{80}{100}$ $\displaystyle 80:100\rightarrow\frac{80}{100}$

Reduce.

$\frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$ $\displaystyle \frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$

We know that there are 800 $\displaystyle 800$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:800\rightarrow \frac{Red}{800}$ $\displaystyle Red:800\rightarrow \frac{Red}{800}$

Now, we can create a proportion using our two ratios.

$\frac{4}{5}=\frac{Red}{800}$ $\displaystyle \frac{4}{5}=\frac{Red}{800}$

Cross multiply and solve for Red $\displaystyle Red$.

$5 \times Red=4\times800$ $\displaystyle 5 \times Red=4\times800$

Simplify.

$\displaystyle 5 Red=3200$

Divide both sides of the equation by $\displaystyle 5$.

$\frac{5Red}{5}=\frac{3200}{5}$ $\displaystyle \frac{5Red}{5}=\frac{3200}{5}$

Solve.

Red=640 $\displaystyle Red=640$

There are 640 $\displaystyle 640$ red cars in the parking lot.

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Example Question #72 : Ratios & Proportional Relationships

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 3200 $\displaystyle 3200$ cars in the parking lot and $8\%$ $\displaystyle 8\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

182 $\displaystyle 182$

218 $\displaystyle 218$

800 $\displaystyle 800$

256 $\displaystyle 256$

188 $\displaystyle 188$

Correct answer:

256 $\displaystyle 256$

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $8\%$ $\displaystyle 8\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 8$ of them are red. We can write the following ratio:

$8:100\rightarrow\frac{8}{100}$ $\displaystyle 8:100\rightarrow\frac{8}{100}$

Reduce.

$\frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$ $\displaystyle \frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$

We know that there are 3200 $\displaystyle 3200$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:3200\rightarrow \frac{Red}{3200}$ $\displaystyle Red:3200\rightarrow \frac{Red}{3200}$

Now, we can create a proportion using our two ratios.

$\frac{2}{25}=\frac{Red}{3200}$ $\displaystyle \frac{2}{25}=\frac{Red}{3200}$

Cross multiply and solve for Red $\displaystyle Red$.

$25 \times Red=2\times3200$ $\displaystyle 25 \times Red=2\times3200$

Simplify.

$\displaystyle 25 Red=6400$

Divide both sides of the equation by $\displaystyle 25$.

$\frac{25Red}{25}=\frac{6400}{25}$ $\displaystyle \frac{25Red}{25}=\frac{6400}{25}$

Solve.

Red=256 $\displaystyle Red=256$

There are 256 $\displaystyle 256$ red cars in the parking lot.

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Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $98\ inches$ $\displaystyle 98\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$9 \tfrac{5}{6} \ feet$ $\displaystyle 9 \tfrac{5}{6} \ feet$

$8 \tfrac{5}{6} \ feet$ $\displaystyle 8 \tfrac{5}{6} \ feet$

$7 \tfrac{5}{6} \ feet$ $\displaystyle 7 \tfrac{5}{6} \ feet$

$9 \tfrac{1}{6} \ feet$ $\displaystyle 9 \tfrac{1}{6} \ feet$

$8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$

Correct answer:

$8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $98\ inches$ $\displaystyle 98\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$98\ inches:x\ feet\rightarrow \frac{98\ inches}{x\ feet}$ $\displaystyle 98\ inches:x\ feet\rightarrow \frac{98\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{98\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{98\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=98\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=98\ inches \times (1\ foot)$

Simplify.

12x=98 $\displaystyle 12x=98$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{98}{12}$ $\displaystyle \frac{12x}{12}=\frac{98}{12}$

Solve.

$x=8 \tfrac{2}{12} \ feet$ $\displaystyle x=8 \tfrac{2}{12} \ feet$

Reduce.

$x=8 \tfrac{1}{6} \ feet$ $\displaystyle x=8 \tfrac{1}{6} \ feet$

The carpenter needs $8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$ of material.

Report an Error

Example Question #2 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $124\ inches$ $\displaystyle 124\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$10 \tfrac{1}{3} \ feet$ $\displaystyle 10 \tfrac{1}{3} \ feet$

$9 \tfrac{2}{3} \ feet$ $\displaystyle 9 \tfrac{2}{3} \ feet$

$11 \tfrac{1}{3} \ feet$ $\displaystyle 11 \tfrac{1}{3} \ feet$

$10 \tfrac{3}{5} \ feet$ $\displaystyle 10 \tfrac{3}{5} \ feet$

$10 \tfrac{2}{3} \ feet$ $\displaystyle 10 \tfrac{2}{3} \ feet$

Correct answer:

$10 \tfrac{1}{3} \ feet$ $\displaystyle 10 \tfrac{1}{3} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $124\ inches$ $\displaystyle 124\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$124\ inches:x\ feet\rightarrow \frac{124\ inches}{x\ feet}$ $\displaystyle 124\ inches:x\ feet\rightarrow \frac{124\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{124\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{124\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=124\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=124\ inches \times (1\ foot)$

Simplify.

12x=124 $\displaystyle 12x=124$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{124}{12}$ $\displaystyle \frac{12x}{12}=\frac{124}{12}$

Solve.

$x=10 \tfrac{4}{12} \ feet$ $\displaystyle x=10 \tfrac{4}{12} \ feet$

Reduce.

$x=10 \tfrac{1}{3} \ feet$ $\displaystyle x=10 \tfrac{1}{3} \ feet$

The carpenter needs $10 \tfrac{1}{3} \ feet$ $\displaystyle 10 \tfrac{1}{3} \ feet$ of material.

Report an Error

Example Question #91 : Ratio And Proportion

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $39\ inches$ $\displaystyle 39\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$3 \tfrac{2}{5} \ feet$ $\displaystyle 3 \tfrac{2}{5} \ feet$

$3 \tfrac{1}{5} \ feet$ $\displaystyle 3 \tfrac{1}{5} \ feet$

$3 \tfrac{1}{2} \ feet$ $\displaystyle 3 \tfrac{1}{2} \ feet$

$3 \tfrac{3}{4} \ feet$ $\displaystyle 3 \tfrac{3}{4} \ feet$

$3 \tfrac{1}{4} \ feet$ $\displaystyle 3 \tfrac{1}{4} \ feet$

Correct answer:

$3 \tfrac{1}{4} \ feet$ $\displaystyle 3 \tfrac{1}{4} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $39\ inches$ $\displaystyle 39\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$39\ inches:x\ feet\rightarrow \frac{39\ inches}{x\ feet}$ $\displaystyle 39\ inches:x\ feet\rightarrow \frac{39\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{39\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{39\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=39\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=39\ inches \times (1\ foot)$

Simplify.

12x=39 $\displaystyle 12x=39$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{39}{12}$ $\displaystyle \frac{12x}{12}=\frac{39}{12}$

Solve.

$x=3 \tfrac{3}{12} \ feet$ $\displaystyle x=3 \tfrac{3}{12} \ feet$

Reduce.

$x=3 \tfrac{1}{4} \ feet$ $\displaystyle x=3 \tfrac{1}{4} \ feet$

The carpenter needs $3 \tfrac{1}{4} \ feet$ $\displaystyle 3 \tfrac{1}{4} \ feet$ of material.

Report an Error

Example Question #2 : Solving Word Problems With One Unit Conversions

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $87\ inches$ $\displaystyle 87\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$7 \tfrac{1}{4} \ feet$ $\displaystyle 7 \tfrac{1}{4} \ feet$

$7 \tfrac{2}{5} \ feet$ $\displaystyle 7 \tfrac{2}{5} \ feet$

$6 \tfrac{3}{4} \ feet$ $\displaystyle 6 \tfrac{3}{4} \ feet$

$8 \tfrac{1}{5} \ feet$ $\displaystyle 8 \tfrac{1}{5} \ feet$

$8 \tfrac{1}{4} \ feet$ $\displaystyle 8 \tfrac{1}{4} \ feet$

Correct answer:

$7 \tfrac{1}{4} \ feet$ $\displaystyle 7 \tfrac{1}{4} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $87\ inches$ $\displaystyle 87\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$87\ inches:x\ feet\rightarrow \frac{87\ inches}{x\ feet}$ $\displaystyle 87\ inches:x\ feet\rightarrow \frac{87\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{87\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{87\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=87\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=87\ inches \times (1\ foot)$

Simplify.

12x=87 $\displaystyle 12x=87$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{87}{12}$ $\displaystyle \frac{12x}{12}=\frac{87}{12}$

Solve.

$x=7 \tfrac{3}{12} \ feet$ $\displaystyle x=7 \tfrac{3}{12} \ feet$

Reduce.

$x=7 \tfrac{1}{4} \ feet$ $\displaystyle x=7 \tfrac{1}{4} \ feet$

The carpenter needs $7 \tfrac{1}{4} \ feet$ $\displaystyle 7 \tfrac{1}{4} \ feet$ of material.

Report an Error

Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $144\ inches$ $\displaystyle 144\ inches$ of the moulding for the house. How many additional feet of the material will he need to purchase to finish the model?

Possible Answers:

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 10$

$\displaystyle 4$

$\displaystyle 2$

Correct answer:

$\displaystyle 4$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $144\ inches$ $\displaystyle 144\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$144\ inches:x\ feet\rightarrow \frac{144\ inches}{x\ feet}$ $\displaystyle 144\ inches:x\ feet\rightarrow \frac{144\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{144\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{144\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=144\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=144\ inches \times (1\ foot)$

Simplify.

12x=144 $\displaystyle 12x=144$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{144}{12}$ $\displaystyle \frac{12x}{12}=\frac{144}{12}$

Solve.

$x=12 \ feet$ $\displaystyle x=12 \ feet$

The carpenter needs $12 \ feet$ $\displaystyle 12 \ feet$ of material. Since he already has 8 feet $\displaystyle 8 feet$ he will need to purchase $\displaystyle 4$ more to finish the project.

Report an Error

Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\ feet$ $\displaystyle 8\ feet$ of crown moulding to use as accent pieces. He needs $164\ inches$ $\displaystyle 164\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$12 \tfrac{1}{3} \ feet$ $\displaystyle 12 \tfrac{1}{3} \ feet$

$13 \tfrac{1}{5} \ feet$ $\displaystyle 13 \tfrac{1}{5} \ feet$

$11 \tfrac{2}{3} \ feet$ $\displaystyle 11 \tfrac{2}{3} \ feet$

$13 \tfrac{2}{3} \ feet$ $\displaystyle 13 \tfrac{2}{3} \ feet$

$13 \tfrac{1}{3} \ feet$ $\displaystyle 13 \tfrac{1}{3} \ feet$

Correct answer:

$13 \tfrac{2}{3} \ feet$ $\displaystyle 13 \tfrac{2}{3} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $164\ inches$ $\displaystyle 164\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$164\ inches:x\ feet\rightarrow \frac{164\ inches}{x\ feet}$ $\displaystyle 164\ inches:x\ feet\rightarrow \frac{164\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{164\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{164\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=164\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=164\ inches \times (1\ foot)$

Simplify.

12x=164 $\displaystyle 12x=164$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{164}{12}$ $\displaystyle \frac{12x}{12}=\frac{164}{12}$

Solve.

$x=13 \tfrac{8}{12} \ feet$ $\displaystyle x=13 \tfrac{8}{12} \ feet$

Reduce.

$x=13 \tfrac{2}{3} \ feet$ $\displaystyle x=13 \tfrac{2}{3} \ feet$

The carpenter needs $13 \tfrac{2}{3} \ feet$ $\displaystyle 13 \tfrac{2}{3} \ feet$ of material.

Report an Error

Example Question #2 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\textup{ feet}$ $\displaystyle 8\textup{ feet}$ of crown molding to use as accent pieces. He needs $18\textup{ inches}$ $\displaystyle 18\textup{ inches}$ of the molding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$2 \tfrac{1}{2} \textup{ feet}$ $\displaystyle 2 \tfrac{1}{2} \textup{ feet}$

$1 \tfrac{2}{3} \textup{ feet}$ $\displaystyle 1 \tfrac{2}{3} \textup{ feet}$

$2 \tfrac{3}{4} \textup{ feet}$ $\displaystyle 2 \tfrac{3}{4} \textup{ feet}$

$3 \tfrac{1}{2} \textup{ feet}$ $\displaystyle 3 \tfrac{1}{2} \textup{ feet}$

$1 \tfrac{1}{2} \textup{ feet}$ $\displaystyle 1 \tfrac{1}{2} \textup{ feet}$

Correct answer:

$1 \tfrac{1}{2} \textup{ feet}$ $\displaystyle 1 \tfrac{1}{2} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $18\ inches$ $\displaystyle 18\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$18\ inches:x\ feet\rightarrow \frac{18\ inches}{x\ feet}$ $\displaystyle 18\ inches:x\ feet\rightarrow \frac{18\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{18\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{18\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=18\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=18\ inches \times (1\ foot)$

Simplify.

12x=18 $\displaystyle 12x=18$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{18}{12}$ $\displaystyle \frac{12x}{12}=\frac{18}{12}$

Solve.

$x=1 \tfrac{1}{2} \ feet$ $\displaystyle x=1 \tfrac{1}{2} \ feet$

The carpenter needs $1 \tfrac{1}{2} \ feet$ $\displaystyle 1 \tfrac{1}{2} \ feet$ of material.

Report an Error

Example Question #73 : Ratios & Proportional Relationships

A carpenter is making a model house and he buys $8\textup{ feet}$ $\displaystyle 8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $9\textup{ inches}$ $\displaystyle 9\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$\frac {1}{4} \textup{ feet}$ $\displaystyle \frac {1}{4} \textup{ feet}$

$\frac {3}{5} \textup{ feet}$ $\displaystyle \frac {3}{5} \textup{ feet}$

$\frac {2}{3} \textup{ feet}$ $\displaystyle \frac {2}{3} \textup{ feet}$

$\frac {3}{4} \textup{ feet}$ $\displaystyle \frac {3}{4} \textup{ feet}$

$\frac {1}{2} \textup{ feet}$ $\displaystyle \frac {1}{2} \textup{ feet}$

Correct answer:

$\frac {3}{4} \textup{ feet}$ $\displaystyle \frac {3}{4} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ $\displaystyle 12\ inches$ in $1\ foot$ $\displaystyle 1\ foot$. We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$ $\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $9 \ inches$ $\displaystyle 9 \ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$9\ inches:x\ feet\rightarrow \frac{9\ inches}{x\ feet}$ $\displaystyle 9\ inches:x\ feet\rightarrow \frac{9\ inches}{x\ feet}$

Now, we can solve for $\displaystyle x$ by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{9\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{9\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=9\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=9\ inches \times (1\ foot)$

Simplify.

12x=9 $\displaystyle 12x=9$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{9}{12}$ $\displaystyle \frac{12x}{12}=\frac{9}{12}$

Solve.

$x=\frac{9}{12} \ feet$ $\displaystyle x=\frac{9}{12} \ feet$

Reduce.

$x=\frac{3}{4} \ feet$ $\displaystyle x=\frac{3}{4} \ feet$

The carpenter needs $\frac {3}{4} \ feet$ $\displaystyle \frac {3}{4} \ feet$ of material.

Report an Error

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All Common Core: 6th Grade Math Resources

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Common Core: 6th Grade Math : Ratios & Proportional Relationships

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #71 : Ratios & Proportional Relationships

Example Question #72 : Ratios & Proportional Relationships

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #2 : Solving Word Problems With One Unit Conversion

Example Question #91 : Ratio And Proportion

Example Question #2 : Solving Word Problems With One Unit Conversions

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #2 : Solving Word Problems With One Unit Conversion

Example Question #73 : Ratios & Proportional Relationships

All Common Core: 6th Grade Math Resources

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