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 #2 : Conversions

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=98

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

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

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=124

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

Example Question #3 : Conversions

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=39

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

Example Question #4 : Conversions

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=87

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

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

A carpenter is making a model house and he buys \displaystyle 8\ feet of crown moulding to use as accent pieces. He needs \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 6

\displaystyle 4

\displaystyle 8

\displaystyle 10

\displaystyle 2

Correct answer:

\displaystyle 4

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=144

Divide both sides by \displaystyle 12.

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

Solve.

\displaystyle x=12 \ feet

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

Example Question #1 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=164

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

Example Question #3 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=18

Divide both sides by \displaystyle 12.

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

Solve.

The carpenter needs  of material.

Example Question #4 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=9

Divide both sides by \displaystyle 12.

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

Solve.

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

Reduce.

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

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

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

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

Possible Answers:

Correct answer:

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 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.

\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.

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=24

Divide both sides by \displaystyle 12.

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

Solve.

\displaystyle x=2 \ feet

The carpenter needs \displaystyle 2 \ feet of material.

Example Question #3 : Solving Word Problems With One Unit Conversions

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

Possible Answers:

Correct answer:

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

Cross multiply and solve for \displaystyle x.

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

Simplify.

\displaystyle 12x=38

Divide both sides by \displaystyle 12.

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

Solve.

Reduce.

The carpenter needs  of material.

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