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2 Diagnostic Tests 27 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

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?

Possible Answers:

$\frac {1}{2} \textup{ feet}$

$\frac {2}{3} \textup{ feet}$

$\frac {3}{5} \textup{ feet}$

$\frac {1}{4} \textup{ feet}$

$\frac {3}{4} \textup{ feet}$

Correct answer:

$\frac {3}{4} \textup{ feet}$

Explanation:

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.

12x=9

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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Example Question #541 : Arithmetic

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?

Possible Answers:

$2 \tfrac{1}{2}\textup{ feet}$

$2 \tfrac{3}{4}\textup{ feet}$

$2 \textup{ feet}$

$1 \tfrac{1}{2}\textup{ feet}$

$2 \tfrac{2}{3}\textup{ feet}$

Correct answer:

$2 \textup{ feet}$

Explanation:

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.

12x=24

Divide both sides by .

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

Solve.

$x=2 \ feet$

The carpenter needs $2 \ feet$ of material.

Report an Error

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 $8\textup{ feet}$ 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?

Possible Answers:

$3 \tfrac{5}{6}\textup{ feet}$

$3 \tfrac{3}{4}\textup{ feet}$

$3 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{5}{6}\textup{ feet}$

$3 \tfrac{1}{6}\textup{ feet}$

Correct answer:

$3 \tfrac{1}{6}\textup{ feet}$

Explanation:

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.

12x=38

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.

Report an Error

Example Question #541 : Arithmetic

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?

Possible Answers:

$4 \tfrac{2}{3} \textup{ feet}$

$5 \tfrac{1}{3} \textup{ feet}$

$4 \tfrac{1}{3} \textup{ feet}$

$5 \tfrac{2}{3} \textup{ feet}$

$6 \tfrac{1}{3} \textup{ feet}$

Correct answer:

$5 \tfrac{1}{3} \textup{ feet}$

Explanation:

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.

12x=64

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.

Report an Error

Example Question #542 : Arithmetic

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?

Possible Answers:

$5\textup{ feet}$

$6 \tfrac{1}{3} \textup{ feet}$

$7 \textup{ feet}$

$6 \textup{ feet}$

$4 \textup{ feet}$

Correct answer:

$6 \textup{ feet}$

Explanation:

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.

12x=72

Divide both sides by .

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

Solve.

$x=6 \ feet$

The carpenter needs $6 \ feet$ of material.

Report an Error

Example Question #1 : Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?

Possible Answers:

Correct answer:

Explanation:

In ten years, Mark will be years old, so Mark is 43-10 = 33 years old now, and Brian is one-third of this, or $33 \div 3 = 11$ years old.

Let be the number of years in which Mark will be twice Brian's age. Then Brian will be N + 11 , and Mark will be N + 33 . Since Mark will be twice Brian's age, we can set up and solve the equation:

2 (N + 11) = N + 33

2N + 22 = N + 33

2N + 22-N - 22 = N + 33 -N - 22

N = 11

Mark will be twice Brian's age in years.

Report an Error

Example Question #2 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Possible Answers:

Not enough information is given to determine the answer.

Correct answer:

Explanation:

Since Gary will be 37 in five years, he is 37 - 5 = 32 years old now. He is twice as old as Cathy, so she is $32 \div 2 =16$ years old, and in five years, she will be 16 + 5 = 21 years old.

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Example Question #1 : Solving Linear Equations In Word Problems

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

Possible Answers:

$\$450$

$\$640$

$\$150$

$\$300$

$\$340$

Correct answer:

$\$150$

Explanation:

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

Report an Error

Example Question #1 : Word Problems

Write as an equation:

"Ten added to the product of a number and three is equal to twice the number."

Possible Answers:

3(x+ 10 )= 2x

10x+ 3= 2x

10(x+ 3)= 2x

3x+ 10 = 2x

Correct answer:

3x+ 10 = 2x

Explanation:

Let represent the unknown quantity.

The first expression:

"The product of a number and three" is three times this number, or

"Ten added to the product" is

3x+10

The second expression:

"Twice the number" is two times the number, or

The desired equation is therefore

3x+ 10 = 2x .

Report an Error

Example Question #2 : Word Problems

Write as an equation:

Five-sevenths of the difference of a number and nine is equal to forty.

Possible Answers:

$\frac{5}{7} (y- 9) = 40$

$9 - \frac{5}{7} y = 40$

$\frac{5}{7} y- 9 = 40$

$\frac{5}{7} (9 - y) = 40$

Correct answer:

$\frac{5}{7} (y- 9) = 40$

Explanation:

"The difference of a number and nine" is the result of a subtraction of the two, so we write this as

y- 9

"Five-sevenths of" this difference is the product of $\frac{5}{7}$ and this, or

$\frac{5}{7} (y- 9)$

This is equal to forty, so write the equation as

$\frac{5}{7} (y- 9) = 40$

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All New SAT Math - Calculator Resources

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New SAT Math - Calculator : New SAT Math - Calculator

Study concepts, example questions & explanations for New SAT Math - Calculator

All New SAT Math - Calculator Resources

Example Questions

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

Example Question #541 : Arithmetic

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

Example Question #541 : Arithmetic

Example Question #542 : Arithmetic

Example Question #1 : Word Problems

Example Question #2 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Example Question #1 : Solving Linear Equations In Word Problems

Example Question #1 : Word Problems

Example Question #2 : Word Problems

All New SAT Math - Calculator Resources

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