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New SAT Math - No Calculator : New SAT

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Example Questions

Example Question #2 : Solve Problems Leading To Two Linear Equations: Ccss.Math.Content.8.Ee.C.8c

Adult tickets to the zoo sell for $\$9$ ; child tickets sell for $\$5$ . On a given day, the zoo sold $5\textup,450$ tickets and raised $\$36\textup,330$ in admissions. How many adult tickets were sold?

Possible Answers:

$2\textup,150$

$2\textup,180$

$2\textup,310$

$2\textup,240$

$2\textup,270$

Correct answer:

$2\textup,270$

Explanation:

Let be the number of adult tickets sold. Then the number of child tickets sold is $5\textup,450 - A$ .

The amount of money raised from adult tickets is ; the amount of money raised from child tickets is $5 \left (5\textup,450 - A \right )$ . The sum of these money amounts is $36,330 , so the amount of money raised can be defined by the following equation:

$9A + 5 (5\textup,450-A) = 36\textup,330$

To find the number of adult tickets sold, solve for :

$9A + 27\textup,250-5A = 36\textup,330$

$4A + 27\textup,250 = 36\textup,330$

$4A + 27\textup,250 - 27\textup,250= 36\textup,330- 27\textup,250$

$4A = 9,080\textup$

$4A \div 4 = 9\textup,080 \div 4$

$A = 2\textup,270$

$2\textup,270$ adult tickets were sold.

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Example Question #675 : Algebra

Solve the following story problem:

Jack and Aaron go to the sporting goods store. Jack buys a glove for $\$15$ and wiffle bats for $\$8$ each. Jack has $\$11$ left over. Aaron spends all his money on hats for $\$10$ each and jerseys. Aaron started with $\$30$ more than Jack. How much does one jersey cost?

Possible Answers:

$\$15.00$

$\$40.00$

$\$25.00$

$\$20.00$

$\$13.00$

Correct answer:

$\$20.00$

Explanation:

Let's call "" the cost of one jersey (this is the value we want to find)

Let's call the amount of money Jack starts with ""

Let's call the amount of money Aaron starts with ""

We know Jack buys a glove for $\$15$ and bats for $\$8$ each, and then has $\$11$ left over after. Thus:

J=15+3(8)+11

simplifying, J=$50 so Jack started with $\$50$

We know Aaron buys hats for $\$10$ each and jerseys (unknown cost "") and spends all his money.

A=2(10)+3x

The last important piece of information from the problem is Aaron starts with dollars more than Jack. So:

A=30+J

From before we know:

J=50

Plugging in:

A=30+50

A=80

so Aaron started with $\$80$

Finally we plug $\$80$ into our original equation for A and solve for x:

A=2(10)+3x

80=2(10)+3x

80=20+3x

60=3x

20=x

Thus one jersey costs $\$20.00$

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Example Question #1 : Translating Words To Linear Equations

Read, but do not solve, the following problem:

Adult tickets to the zoo sell for $11; child tickets sell for $7. One day, 6,035 tickets were sold, resulting in $50,713 being raised. How many adult and child tickets were sold?

If and stand for the number of adult and child tickets, respectively, which of the following systems of equations can be used to answer this question?

Possible Answers:

A + C = 50,713

11A + 7C = 6,035

A + C = 6,035

11A - 7C = 50,713

A + C = 6,035

11A + 7C = 50,713

A - C = 50,713

11A + 7C = 6,035

A - C = 6,035

11A + 7C = 50,713

Correct answer:

A + C = 6,035

11A + 7C = 50,713

Explanation:

6,035 total tickets were sold, and the total number of tickets is the sum of the adult and child tickets, A + C .

Therefore, we can say A + C = 6,035 .

The amount of money raised from adult tickets is $11 per ticket mutiplied by tickets, or 11A dollars; similarly, dollars are raised from child tickets. Add these together to get the total amount of money raised:

11A + 7C = 50,713

These two equations form our system of equations.

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Example Question #81 : New Sat Math Calculator

A blue train leaves San Francisco at 8AM going 80 miles per hour. At the same time, a green train leaves Los Angeles, 380 miles away, going 60 miles per hour. Assuming that they are headed towards each other, when will they meet, and about how far away will they be from San Francisco?

Possible Answers:

Around 2:45AM, about 200.15 miles away from San Francisco

Around 10:43AM, about 217.12 miles away from San Francisco

Around 3AM the next day, about 1,520 miles away from San Francisco

The two trains will never meet.

Correct answer:

Around 10:43AM, about 217.12 miles away from San Francisco

Explanation:

This system can be solved a variety of ways, including graphing. To solve algebraically, write an equation for each of the different trains. We will use y to represent the distance from San Francisco, and x to represent the time since 8AM.

The blue train travels 80 miles per hour, so it adds 80 to the distance from San Francisco every hour. Algebraically, this can be written as y=80x .

The green train starts 380 miles away from San Francisco and subtracts distance every hour. This equation should be y=380-60x .

To figure out where these trains' paths will intersect, we can set both right sides equal to each other, since the left side of each is .

80x=380-60x add 60x to both sides

140x = 380 divide both sides by 140

x=2.714

Since we wrote the equation meaning time for , this means that the trains will cross paths after 2.714 hours have gone by. To figure out what time it will be then, figure out how many minutes are in 0.714 hours by multiplying 60*0.714 = 42.857 . So the trains intersect after 2 hours and about 43 minutes, so at 10:43AM.

To figure out how far from San Francisco they are, figure out how many miles the blue train could have gone in 2.714 hours. In other words, plug 2.714 back into the equation y=80x , giving you an answer of y=217.12 .

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Example Question #2092 : Psat Mathematics

How many $\textup { centimeters}$ are in $5\textup { meters?}$

Possible Answers:

$5\textup,000\textup { centimeters}$

$5\textup { centimeters}$

$500\textup { centimeters}$

$1.5\textup { centimeters}$

$50\textup { centimeters}$

Correct answer:

$500\textup { centimeters}$

Explanation:

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 meters will cancel and we are left with $500\ centimeters$

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Example Question #181 : Ratio And Proportion

How many $\textup{centimeters}$ are in $13\textup { meters?}$

Possible Answers:

$130\textup { centimeters}$

$1\textup,300\textup { centimeters}$

$13\textup,000\textup { centimeters}$

$1.3\textup{ centimeters}$

$.0013\textup { centimeters}$

Correct answer:

$1\textup,300\textup { centimeters}$

Explanation:

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 meters will cancel and we are left with $1,300\ centimeters$

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

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?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $98\ inches$ 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.

12x=98

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

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?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $124\ inches$ 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.

12x=124

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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Example Question #753 : Ssat Middle Level Quantitative (Math)

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?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $39\ inches$ 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.

12x=39

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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Example Question #2102 : Psat Mathematics

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?

Possible Answers:

$7 \tfrac{2}{5} \ feet$

$8 \tfrac{1}{5} \ feet$

$7 \tfrac{1}{4} \ feet$

$6 \tfrac{3}{4} \ feet$

$8 \tfrac{1}{4} \ feet$

Correct answer:

$7 \tfrac{1}{4} \ feet$

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 $87\ inches$ 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.

12x=87

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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All New SAT Math - No Calculator Resources

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New SAT Math - No Calculator : New SAT

Study concepts, example questions & explanations for New SAT Math - No Calculator

All New SAT Math - No Calculator Resources

Example Questions

Example Question #2 : Solve Problems Leading To Two Linear Equations: Ccss.Math.Content.8.Ee.C.8c

Example Question #675 : Algebra

Example Question #1 : Translating Words To Linear Equations

Example Question #81 : New Sat Math Calculator

Example Question #2092 : Psat Mathematics

Example Question #181 : Ratio And Proportion

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

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

Example Question #753 : Ssat Middle Level Quantitative (Math)

Example Question #2102 : Psat Mathematics

All New SAT Math - No Calculator Resources

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