Conversions - SAT Math

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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 $24\textup{ inches}$ 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

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

Nancy is visiting her grandmother who lives from her home. Her car’s tank has a full tank ( liters) at the beginning of her drive and uses liter to drive kilometers. How many liters will she need to refill to reach her grandmother’s house with liters left in the tank?

Answer

The correct answer is liters. $\frac{6, kilometers}{1, liter}20, liters=120km$ . . $\frac{1, liter}{6, kilometers}80, kilometers=13.3, liters$ .

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Question

A future pharmacist is unsure what dose they should fill to ensure a patient takes a -mg tablet times a day for one whole week. What is the total dosage they should prescribe?

Answer

The correct answer is mg. $\frac{35, mg}{1, tablet}\frac{4, tablet}{1, day}\frac{7, days}{1, week}=980mg$ .

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Question

A patient is prescribed of a certain drug per day and is allowed to refill his prescription twice. If there are tablets in a prescription, and each tablet has , how many doses are in the prescriptions (original + refills)?

Answer

$3, prescriptions\frac{18, tablets}{1, prescription}\frac{24, mg}{1, tablet}*\frac{1, dose}{16, mg}=81, doses$

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Question

A fruit farm produces strawberries and employs workers. Each worker can pick pounds of berries per hour and work an -hour shift. If each pound of strawberries can be sold for , how much money does the farm make every day?

Answer

The key here is to ensure your units cancel out. $\frac{3, lbs}{1, worker1, hr}\frac{4, dollars}{1, lb}\frac{8, hrs7, workers}{1, day, of, labor}=$672$ .

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Question

A record has a radius of inches with the needle resting on the outer circumference of the record. If the record rotates at a speed of $\frac{\pi }{4}$ radians/sec and it takes minutes to play a full song, how inches of track have been covered by the end of the song?

Answer

Circumference $=2\pi r=10\pi$ inches. The key here is to ensure your units cancel out. $\frac{10\pi , inches}{1, revolution}\frac{1, revolution}{2\pi , radians}\frac{\frac{\pi }{4}, radians}{1, second}\frac{60, seconds}{1, minute}3, minutes=706.5$ inch.

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Question

A student was traveling miles per hour. What is the student’s speed in feet per second?

Answer

$\frac{50, mi}{1, hr}\frac{1, hr}{3600, sec}\frac{5280, ft}{1, mi}=73.3, ft/sec$

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