Solving Word Problems with One Unit Conversions - PSAT Math

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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?

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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.

$x=1 \t$\frac{1}{2}$ \ feet$

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

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?

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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.

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?

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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.

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?

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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.

$x=3 \t$\frac{2}{12}$ \ feet$

Reduce.

$x=3 \t$\frac{1}{6}$ \ feet$

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

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?

Tap to see back →

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.

$x=5 \t$\frac{4}{12}$ \ feet$

Reduce.

$x=5 \t$\frac{1}{3}$ \ feet$

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

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?

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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.

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?

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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.

$x=8 \t$\frac{2}{12}$ \ feet$

Reduce.

$x=8 \t$\frac{1}{6}$ \ feet$

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

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?

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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.

$x=10 \t$\frac{4}{12}$ \ feet$

Reduce.

$x=10 \t$\frac{1}{3}$ \ feet$

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

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?

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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.

$x=3 \t$\frac{3}{12}$ \ feet$

Reduce.

$x=3 \t$\frac{1}{4}$ \ feet$

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

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?

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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.

$x=7 \t$\frac{3}{12}$ \ feet$

Reduce.

$x=7 \t$\frac{1}{4}$ \ feet$

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

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?

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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.

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?

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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.

$x=13 \t$\frac{8}{12}$ \ feet$

Reduce.

$x=13 \t$\frac{2}{3}$ \ feet$

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

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?

Tap to see back →

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.

$x=1 \t$\frac{1}{2}$ \ feet$

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

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?

Tap to see back →

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.

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?

Tap to see back →

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.

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?

Tap to see back →

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.

$x=3 \t$\frac{2}{12}$ \ feet$

Reduce.

$x=3 \t$\frac{1}{6}$ \ feet$

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

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?

Tap to see back →

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.

$x=5 \t$\frac{4}{12}$ \ feet$

Reduce.

$x=5 \t$\frac{1}{3}$ \ feet$

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

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?

Tap to see back →

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.

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?

Tap to see back →

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.

$x=8 \t$\frac{2}{12}$ \ feet$

Reduce.

$x=8 \t$\frac{1}{6}$ \ feet$

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

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?

Tap to see back →

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.

$x=10 \t$\frac{4}{12}$ \ feet$

Reduce.

$x=10 \t$\frac{1}{3}$ \ feet$

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