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SSAT Middle Level Math : Ratio and Proportion

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Example Questions

Example Question #81 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 164 $\displaystyle 164$ cars in the parking lot and $25 \%$ $\displaystyle 25 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

$\displaystyle 41$

$\displaystyle 33$

$\displaystyle 47$

$\displaystyle 36$

$\displaystyle 52$

Correct answer:

$\displaystyle 41$

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 $25\%$ $\displaystyle 25\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 25$ of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$ $\displaystyle 25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$ $\displaystyle \frac{25}{100}\rightarrow \frac{1}{4}$

We know that there are 164 $\displaystyle 164$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:164\rightarrow \frac{Red}{164}$ $\displaystyle Red:164\rightarrow \frac{Red}{164}$

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

$\frac{1}{4}=\frac{Red}{164}$ $\displaystyle \frac{1}{4}=\frac{Red}{164}$

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

$4 \times Red=1\times164$ $\displaystyle 4 \times Red=1\times164$

Simplify.

$\displaystyle 4 Red=164$

Divide both sides of the equation by $\displaystyle 4$.

$\frac{4Red}{4}=\frac{164}{4}$ $\displaystyle \frac{4Red}{4}=\frac{164}{4}$

Solve.

Red=41 $\displaystyle Red=41$

There are $\displaystyle 41$ red cars in the parking lot.

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Example Question #82 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 135 $\displaystyle 135$ cars in the parking lot and $60 \%$ $\displaystyle 60 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

$\displaystyle 79$

$\displaystyle 81$

$\displaystyle 72$

$\displaystyle 60$

$\displaystyle 93$

Correct answer:

$\displaystyle 81$

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 $60\%$ $\displaystyle 60\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 60$ of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$ $\displaystyle 60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$ $\displaystyle \frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

We know that there are 135 $\displaystyle 135$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:135\rightarrow \frac{Red}{135}$ $\displaystyle Red:135\rightarrow \frac{Red}{135}$

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

$\frac{3}{5}=\frac{Red}{135}$ $\displaystyle \frac{3}{5}=\frac{Red}{135}$

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

$5 \times Red=3\times135$ $\displaystyle 5 \times Red=3\times135$

Simplify.

$\displaystyle 5 Red=405$

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

$\frac{5Red}{5}=\frac{405}{5}$ $\displaystyle \frac{5Red}{5}=\frac{405}{5}$

Solve.

Red=81 $\displaystyle Red=81$

There are $\displaystyle 81$ red cars in the parking lot.

Report an Error

Example Question #243 : Numbers And Operations

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 400 $\displaystyle 400$ cars in the parking lot and $40 \%$ $\displaystyle 40 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

148 $\displaystyle 148$

$\displaystyle 61$

160 $\displaystyle 160$

164 $\displaystyle 164$

116 $\displaystyle 116$

Correct answer:

160 $\displaystyle 160$

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 $40\%$ $\displaystyle 40\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 40$ of them are red. We can write the following ratio:

$40:100\rightarrow\frac{40}{100}$ $\displaystyle 40:100\rightarrow\frac{40}{100}$

Reduce.

$\frac{40}{100}\rightarrow \frac{4}{10}\rightarrow \frac{2}{5}$ $\displaystyle \frac{40}{100}\rightarrow \frac{4}{10}\rightarrow \frac{2}{5}$

We know that there are 400 $\displaystyle 400$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:400\rightarrow \frac{Red}{400}$ $\displaystyle Red:400\rightarrow \frac{Red}{400}$

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

$\frac{2}{5}=\frac{Red}{400}$ $\displaystyle \frac{2}{5}=\frac{Red}{400}$

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

$5 \times Red=2\times400$ $\displaystyle 5 \times Red=2\times400$

Simplify.

$\displaystyle 5 Red=800$

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

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

Solve.

Red=160 $\displaystyle Red=160$

There are 160 $\displaystyle 160$ red cars in the parking lot.

Report an Error

Example Question #22 : Percentage

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 200 $\displaystyle 200$ cars in the parking lot and $50 \%$ $\displaystyle 50 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

102 $\displaystyle 102$

210 $\displaystyle 210$

100 $\displaystyle 100$

120 $\displaystyle 120$

Correct answer:

100 $\displaystyle 100$

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 $50\%$ $\displaystyle 50\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 50$ of them are red. We can write the following ratio:

$50:100\rightarrow\frac{50}{100}$ $\displaystyle 50:100\rightarrow\frac{50}{100}$

Reduce.

$\frac{50}{100}\rightarrow \frac{5}{10}\rightarrow \frac{1}{2}$ $\displaystyle \frac{50}{100}\rightarrow \frac{5}{10}\rightarrow \frac{1}{2}$

We know that there are 200 $\displaystyle 200$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:200\rightarrow \frac{Red}{200}$ $\displaystyle Red:200\rightarrow \frac{Red}{200}$

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

$\frac{1}{2}=\frac{Red}{200}$ $\displaystyle \frac{1}{2}=\frac{Red}{200}$

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

$2 \times Red=1\times200$ $\displaystyle 2 \times Red=1\times200$

Simplify.

$\displaystyle 2 Red=200$

Divide both sides of the equation by $\displaystyle 2$.

$\frac{2Red}{2}=\frac{200}{2}$ $\displaystyle \frac{2Red}{2}=\frac{200}{2}$

Solve.

Red=100 $\displaystyle Red=100$

There are 100 $\displaystyle 100$ red cars in the parking lot.

Report an Error

Example Question #85 : Numbers And Operations

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 300 $\displaystyle 300$ cars in the parking lot and $30 \%$ $\displaystyle 30 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

$\displaystyle 99$

$\displaystyle 90$

$\displaystyle 72$

$\displaystyle 81$

$\displaystyle 74$

Correct answer:

$\displaystyle 90$

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 $30\%$ $\displaystyle 30\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 30$ of them are red. We can write the following ratio:

$30:100\rightarrow\frac{30}{100}$ $\displaystyle 30:100\rightarrow\frac{30}{100}$

Reduce.

$\frac{30}{100}\rightarrow \frac{3}{10}$ $\displaystyle \frac{30}{100}\rightarrow \frac{3}{10}$

We know that there are 300 $\displaystyle 300$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:300\rightarrow \frac{Red}{300}$ $\displaystyle Red:300\rightarrow \frac{Red}{300}$

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

$\frac{3}{10}=\frac{Red}{300}$ $\displaystyle \frac{3}{10}=\frac{Red}{300}$

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

$10 \times Red=3\times300$ $\displaystyle 10 \times Red=3\times300$

Simplify.

$\displaystyle 10 Red=900$

Divide both sides of the equation by $\displaystyle 10$.

$\frac{10Red}{10}=\frac{900}{10}$ $\displaystyle \frac{10Red}{10}=\frac{900}{10}$

Solve.

Red=90 $\displaystyle Red=90$

There are $\displaystyle 90$ red cars in the parking lot.

Report an Error

Example Question #83 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 400 $\displaystyle 400$ cars in the parking lot and $4 \%$ $\displaystyle 4 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

$\displaystyle 18$

$\displaystyle 16$

$\displaystyle 24$

$\displaystyle 8$

$\displaystyle 36$

Correct answer:

$\displaystyle 16$

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 $4\%$ $\displaystyle 4\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 4$ of them are red. We can write the following ratio:

$4:100\rightarrow\frac{4}{100}$ $\displaystyle 4:100\rightarrow\frac{4}{100}$

Reduce.

$\frac{4}{100}\rightarrow \frac{2}{50}\rightarrow \frac{1}{25}$ $\displaystyle \frac{4}{100}\rightarrow \frac{2}{50}\rightarrow \frac{1}{25}$

We know that there are 400 $\displaystyle 400$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:40\rightarrow \frac{Red}{400}$ $\displaystyle Red:40\rightarrow \frac{Red}{400}$

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

$\frac{1}{25}=\frac{Red}{400}$ $\displaystyle \frac{1}{25}=\frac{Red}{400}$

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

$25 \times Red=1\times400$ $\displaystyle 25 \times Red=1\times400$

Simplify.

$\displaystyle 25 Red=400$

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

$\frac{25Red}{25}=\frac{400}{25}$ $\displaystyle \frac{25Red}{25}=\frac{400}{25}$

Solve.

Red=16 $\displaystyle Red=16$

There are $\displaystyle 16$ red cars in the parking lot.

Report an Error

Example Question #64 : Grade 6

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 200 $\displaystyle 200$ cars in the parking lot and $35 \%$ $\displaystyle 35 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

$\displaystyle 72$

$\displaystyle 70$

$\displaystyle 35$

$\displaystyle 80$

$\displaystyle 89$

Correct answer:

$\displaystyle 70$

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 $35\%$ $\displaystyle 35\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 35$ of them are red. We can write the following ratio:

$35:100\rightarrow\frac{35}{100}$ $\displaystyle 35:100\rightarrow\frac{35}{100}$

Reduce.

$\frac{35}{100}\rightarrow \frac{7}{20}$ $\displaystyle \frac{35}{100}\rightarrow \frac{7}{20}$

We know that there are 200 $\displaystyle 200$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:200\rightarrow \frac{Red}{200}$ $\displaystyle Red:200\rightarrow \frac{Red}{200}$

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

$\frac{7}{20}=\frac{Red}{200}$ $\displaystyle \frac{7}{20}=\frac{Red}{200}$

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

$20 \times Red=7\times200$ $\displaystyle 20 \times Red=7\times200$

Simplify.

$\displaystyle 20Red=1400$

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

$\frac{20Red}{20}=\frac{1400}{20}$ $\displaystyle \frac{20Red}{20}=\frac{1400}{20}$

Solve.

Red=70 $\displaystyle Red=70$

There are $\displaystyle 70$ red cars in the parking lot.

Report an Error

Example Question #84 : Ratio And Proportion

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:

$\displaystyle 80$

640 $\displaystyle 640$

460 $\displaystyle 460$

360 $\displaystyle 360$

630 $\displaystyle 630$

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.

Report an Error

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

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

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 moulding to use as accent pieces. He needs $24\textup{ inches}$ $\displaystyle 24\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $24\ inches$ $\displaystyle 24\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

$24\ inches:x\ feet\rightarrow \frac{24\ inches}{x\ feet}$ $\displaystyle 24\ inches:x\ feet\rightarrow \frac{24\ inches}{x\ feet}$

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

$\frac{12\ inches}{1\ foot}=\frac{24\ inches}{x\ feet}$ $\displaystyle \frac{12\ inches}{1\ foot}=\frac{24\ inches}{x\ feet}$

Cross multiply and solve for $\displaystyle x$.

$12\ inches \times (x\ feet)=24\ inches \times (1\ foot)$ $\displaystyle 12\ inches \times (x\ feet)=24\ inches \times (1\ foot)$

Simplify.

12x=24 $\displaystyle 12x=24$

Divide both sides by $\displaystyle 12$.

$\frac{12x}{12}=\frac{24}{12}$ $\displaystyle \frac{12x}{12}=\frac{24}{12}$

Solve.

$x=2 \ feet$ $\displaystyle x=2 \ feet$

The carpenter needs $2 \ feet$ $\displaystyle 2 \ feet$ of material.

Report an Error

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SSAT Middle Level Math : Ratio and Proportion

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #81 : Ratio And Proportion

Example Question #82 : Ratio And Proportion

Example Question #243 : Numbers And Operations

Example Question #22 : Percentage

Example Question #85 : Numbers And Operations

Example Question #83 : Ratio And Proportion

Example Question #64 : Grade 6

Example Question #84 : Ratio And Proportion

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

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

All SSAT Middle Level Math Resources

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