Conversions - SAT Math

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Question

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $24\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Answer

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

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

We know that the carpenter needs $24\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

$x=2 \ feet$

The carpenter needs $2 \ feet$ of material.

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Question

How many $\textup{centimeters}$ are in $13\textup { meters?}$

Answer

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The will cancel and we are left with $1,300\ centimeters$

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Question

How many $\textup { centimeters}$ are in $5\textup { meters?}$

Answer

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$

The will cancel and we are left with $500\ centimeters$

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $38\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Answer

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

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

We know that the carpenter needs $38\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$38\ inches:x\ feet\rightarrow \frac{38\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{38\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=38\ inches \times (1\ foot)$

Simplify.

Divide both sides by .

$\frac{12x}{12}=\frac{38}{12}$

Solve.

$x=3 \tfrac{2}{12} \ feet$

Reduce.

$x=3 \tfrac{1}{6} \ feet$

The carpenter needs $3 \tfrac{1}{6} \ feet$ of material.

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Question

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

Answer

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

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

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

$64\ inches:x\ feet\rightarrow \frac{64\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{64\ inches}{x\ feet}$

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

$\frac{12x}{12}=\frac{64}{12}$

Solve.

$x=5 \tfrac{4}{12} \ feet$

Reduce.

$x=5 \tfrac{1}{3} \ feet$

The carpenter needs $5 \tfrac{1}{3} \ feet$ of material.

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Question

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

Answer

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

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

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

$72\ inches:x\ feet\rightarrow \frac{72\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{72\ inches}{x\ feet}$

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

$\frac{12x}{12}=\frac{72}{12}$

Solve.

$x=6 \ feet$

The carpenter needs $6 \ feet$ of material.

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

$x=12 \ feet$

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

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Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

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Question

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $24\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Answer

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

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

We know that the carpenter needs $24\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

$x=2 \ feet$

The carpenter needs $2 \ feet$ of material.

Compare your answer with the correct one above

Question

How many $\textup{centimeters}$ are in $13\textup { meters?}$

Answer

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The will cancel and we are left with $1,300\ centimeters$

Compare your answer with the correct one above

Question

How many $\textup { centimeters}$ are in $5\textup { meters?}$

Answer

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$

The will cancel and we are left with $500\ centimeters$

Compare your answer with the correct one above

Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

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

Now, we can solve for by creating a proportion using our two ratios.

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

Cross multiply and solve for .

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

Simplify.

Divide both sides by .

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

Solve.

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

Reduce.

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

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

Compare your answer with the correct one above

Question

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $38\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Answer

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

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

We know that the carpenter needs $38\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$38\ inches:x\ feet\rightarrow \frac{38\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{38\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=38\ inches \times (1\ foot)$

Simplify.

Divide both sides by .

$\frac{12x}{12}=\frac{38}{12}$

Solve.

$x=3 \tfrac{2}{12} \ feet$

Reduce.

$x=3 \tfrac{1}{6} \ feet$

The carpenter needs $3 \tfrac{1}{6} \ feet$ of material.

Compare your answer with the correct one above

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