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Flashcards: Solving Word Problems with One Unit Conversion

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

$9 \tfrac{1}{6} \ feet$ $\displaystyle 9 \tfrac{1}{6} \ feet$

$7 \tfrac{5}{6} \ feet$ $\displaystyle 7 \tfrac{5}{6} \ feet$

$8 \tfrac{5}{6} \ feet$ $\displaystyle 8 \tfrac{5}{6} \ feet$

$8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$

$9 \tfrac{5}{6} \ feet$ $\displaystyle 9 \tfrac{5}{6} \ feet$

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Flashcards: Solving Word Problems with One Unit Conversion

$9 \tfrac{1}{6} \ feet$ $\displaystyle 9 \tfrac{1}{6} \ feet$

$7 \tfrac{5}{6} \ feet$ $\displaystyle 7 \tfrac{5}{6} \ feet$

$8 \tfrac{5}{6} \ feet$ $\displaystyle 8 \tfrac{5}{6} \ feet$

$8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$

$9 \tfrac{5}{6} \ feet$ $\displaystyle 9 \tfrac{5}{6} \ feet$

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Flashcards: Solving Word Problems with One Unit Conversion

Your answer:

$9 \tfrac{1}{6} \ feet$ $\displaystyle 9 \tfrac{1}{6} \ feet$

Your answer:

$7 \tfrac{5}{6} \ feet$ $\displaystyle 7 \tfrac{5}{6} \ feet$

Your answer:

$8 \tfrac{5}{6} \ feet$ $\displaystyle 8 \tfrac{5}{6} \ feet$

Your answer:

$9 \tfrac{5}{6} \ feet$ $\displaystyle 9 \tfrac{5}{6} \ feet$

Correct answer:

$8 \tfrac{1}{6} \ feet$ $\displaystyle 8 \tfrac{1}{6} \ feet$

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 $98\ inches$ $\displaystyle 98\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

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

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

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

Cross multiply and solve for $\displaystyle x$ .

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

Simplify.

12x=98 $\displaystyle 12x=98$

Divide both sides by $\displaystyle 12$ .

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

Solve.

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

Reduce.

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

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

Flashcards: Solving Word Problems with One Unit Conversion

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

$10 \tfrac{3}{5} \ feet$ $\displaystyle 10 \tfrac{3}{5} \ feet$

$11 \tfrac{1}{3} \ feet$ $\displaystyle 11 \tfrac{1}{3} \ feet$

$9 \tfrac{2}{3} \ feet$ $\displaystyle 9 \tfrac{2}{3} \ feet$

$10 \tfrac{2}{3} \ feet$ $\displaystyle 10 \tfrac{2}{3} \ feet$

$10 \tfrac{1}{3} \ feet$ $\displaystyle 10 \tfrac{1}{3} \ feet$

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Flashcards: Solving Word Problems with One Unit Conversion

Your answer:

$10 \tfrac{3}{5} \ feet$ $\displaystyle 10 \tfrac{3}{5} \ feet$

Your answer:

$11 \tfrac{1}{3} \ feet$ $\displaystyle 11 \tfrac{1}{3} \ feet$

Your answer:

$9 \tfrac{2}{3} \ feet$ $\displaystyle 9 \tfrac{2}{3} \ feet$

Your answer:

$10 \tfrac{2}{3} \ feet$ $\displaystyle 10 \tfrac{2}{3} \ feet$

Correct answer:

$10 \tfrac{1}{3} \ feet$ $\displaystyle 10 \tfrac{1}{3} \ feet$

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 $124\ inches$ $\displaystyle 124\ inches$ of material to finish the house. We can write this as a ratio using the variable $\displaystyle x$ to substitute the amount of feet.

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

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

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

Cross multiply and solve for $\displaystyle x$ .

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

Simplify.

12x=124 $\displaystyle 12x=124$

Divide both sides by $\displaystyle 12$ .

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

Solve.

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

Reduce.

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

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

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