New SAT Math - Calculator : Solving Word Problems with One Unit Conversion

Study concepts, example questions & explanations for New SAT Math - Calculator

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Example Questions

Example Question #91 : Ratio And Proportion

A carpenter is making a model house and he buys \(\displaystyle 8\textup{ feet}\) of crown moulding to use as accent pieces. He needs \(\displaystyle 64\textup{ inches}\) of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

\(\displaystyle 5 \tfrac{2}{3} \textup{ feet}\)

\(\displaystyle 4 \tfrac{2}{3} \textup{ feet}\)

\(\displaystyle 5 \tfrac{1}{3} \textup{ feet}\)

\(\displaystyle 4 \tfrac{1}{3} \textup{ feet}\)

\(\displaystyle 6 \tfrac{1}{3} \textup{ feet}\)

Correct answer:

\(\displaystyle 5 \tfrac{1}{3} \textup{ feet}\)

Explanation:

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

\(\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}\)

We know that the carpenter needs \(\displaystyle 64\ inches\) of material to finish the house. We can write this as a ratio using the variable \(\displaystyle x\) to substitute the amount of feet.

\(\displaystyle 64\ inches:x\ feet\rightarrow \frac{64\ inches}{x\ feet}\)

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

\(\displaystyle \frac{12\ inches}{1\ foot}=\frac{64\ inches}{x\ feet}\)

Cross multiply and solve for \(\displaystyle x\).

\(\displaystyle 12\ inches \times (x\ feet)=64\ inches \times (1\ foot)\)

Simplify.

\(\displaystyle 12x=64\)

Divide both sides by \(\displaystyle 12\).

\(\displaystyle \frac{12x}{12}=\frac{64}{12}\)

Solve.

\(\displaystyle x=5 \tfrac{4}{12} \ feet\)

Reduce.

\(\displaystyle x=5 \tfrac{1}{3} \ feet\)

The carpenter needs \(\displaystyle 5 \tfrac{1}{3} \ feet\) of material.

Example Question #92 : Ratio And Proportion

A carpenter is making a model house and he buys \(\displaystyle 8\textup{ feet}\) of crown moulding to use as accent pieces. He needs \(\displaystyle 72\textup{ inches}\) of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

\(\displaystyle 6 \textup{ feet}\)

\(\displaystyle 4 \textup{ feet}\)

\(\displaystyle 5\textup{ feet}\)

\(\displaystyle 7 \textup{ feet}\)

\(\displaystyle 6 \tfrac{1}{3} \textup{ feet}\)

Correct answer:

\(\displaystyle 6 \textup{ feet}\)

Explanation:

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

\(\displaystyle 12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}\)

We know that the carpenter needs \(\displaystyle 72\ inches\) of material to finish the house. We can write this as a ratio using the variable \(\displaystyle x\) to substitute the amount of feet.

\(\displaystyle 72\ inches:x\ feet\rightarrow \frac{72\ inches}{x\ feet}\)

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

\(\displaystyle \frac{12\ inches}{1\ foot}=\frac{72\ inches}{x\ feet}\)

Cross multiply and solve for \(\displaystyle x\).

\(\displaystyle 12\ inches \times (x\ feet)=72\ inches \times (1\ foot)\)

Simplify.

\(\displaystyle 12x=72\)

Divide both sides by \(\displaystyle 12\).

\(\displaystyle \frac{12x}{12}=\frac{72}{12}\)

Solve.

\(\displaystyle x=6 \ feet\)

The carpenter needs \(\displaystyle 6 \ feet\) of material.

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