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HSPT Math : Problem Solving

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Example Questions

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Example Question #3 : How To Solve One Step Equations

A full helium tank can blow up 50 balloons. At least how many times does the tank have to be re-filled in order to blow up 140 balloons?

Possible Answers:

Correct answer:

Explanation:

Divide $140\div 50=2.8$

Answer: The tank must be filled up at least 3 times.

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Example Question #1 : How To Solve One Step Equations

Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?

Possible Answers:

60 dollars

30 dollars

22 dollars

20 dollars

Correct answer:

22 dollars

Explanation:

Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.

Below are the prices that will be charged based on this make up:

2 pairs of people at 40 dollars per pair = 80 dollars

1 solo person at 30 dollars per person = 30 dollars

80 dollars plus 30 dollars is 110 dollars, the grand total.

When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.

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Example Question #1 : How To Find The Solution To An Equation

Ann, Bailey, Cara, Jack, and Jill are running a marathon. Cara finishes 4 minutes before Ann. Jill finishes after Bailey, who finishes after Ann. Jack finishes right before Bailey. Who else does Jack finish the race before?

Possible Answers:

There is not enough information to solve this problem.

Bailey

Cara

Jill

Ann

Correct answer:

Jill

Explanation:

Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.

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Example Question #1 : Algebra

Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are $2.50 per pound, apples cost $1.50 per pound and bananas are $0.50 per pound. Which combination of fruit will fit her budget?

Possible Answers:

1 pound of oranges, 1.5 pounds of apples and 1.5 pounds of bananas

1 pound of oranges, 1 pound of apples and 2 pounds of bananas

2 pounds of oranges and 1 pound of apples

3 pounds of apples and 2 pounds of bananas

1.5 pounds of oranges and 4 pounds of bananas

Correct answer:

1 pound of oranges, 1 pound of apples and 2 pounds of bananas

Explanation:

Make a simple algebra equation and test it against each combination:

Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)

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Example Question #2 : How To Solve One Step Equations

Solve: 8x=3200

Possible Answers:

y=3192

x=400

x=3208

y=400

x=3192

Correct answer:

x=400

Explanation:

To solve for , divide by eight on both sides of the equation.

$\frac{8x}{8}=\frac{3200}{8}$

x=400

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Example Question #3 : How To Solve One Step Equations

Solve for : $-\frac{y}{3} = 2$

Possible Answers:

$\frac{1}{6}$

$-\frac{1}{6}$

Correct answer:

Explanation:

To isolate the unknown variable, multiply both sides by negative three.

$-\frac{y}{3} \times -3= 2 \times -3$

y=-6

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Example Question #4 : How To Solve One Step Equations

Solve: $4x = \frac{1}{8}$

Possible Answers:

$\frac{1}{12}$

$\frac{1}{32}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{32}$

Explanation:

To isolate the unknown variable, multiply both sides by one-fourth.

$4x \times (\frac{1}{4})= \frac{1}{8}\times (\frac{1}{4})$

$x=\frac{1}{32}$

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Example Question #11 : How To Solve One Step Equations

Solve: $\frac{x}{0.02} = 50$

Possible Answers:

100

$\frac{1}{100}$

$\frac{1}{50}$

Correct answer:

Explanation:

Multiply 0.02 on both sides of the equation to isolate the variable.

$\frac{x}{0.02} \times 0.02= 50\times 0.02$

x=1

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Example Question #12 : Algebra

Solve for :

a+32 = 32

Possible Answers:

$-\frac{1}{32}$

$\frac{1}{32}$

Correct answer:

Explanation:

In order to solve this equation we need to isolate the variable to one side. Do not forget to perform the same operation on both sides of the equation.

a+32 = 32

Subtract from both sides of the equation.

a+32- (32)= 32-(32)

Solve.

a=0

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Example Question #1 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Let be the temperature expressed in degrees Celsius. Then the equivalent temperature in degrees Fahrenheit can be calculated using the formula:

$F = \frac{9}{5} C + 32$

What is $65^{\circ } C$ expressed in degrees Fahrenheit?

Possible Answers:

$149 ^{\circ } F$

$174.6^{\circ } F$

$59.4^{\circ } F$

$85 ^{\circ } F$

Correct answer:

$149 ^{\circ } F$

Explanation:

$F = \frac{9}{5} C + 32$

$F = \frac{9}{5} \cdot 65 + 32 = 117+32 = 149 ^{\circ } F$

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HSPT Math : Problem Solving

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #3 : How To Solve One Step Equations

Example Question #1 : How To Solve One Step Equations

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : Algebra

Example Question #2 : How To Solve One Step Equations

Example Question #3 : How To Solve One Step Equations

Example Question #4 : How To Solve One Step Equations

Example Question #11 : How To Solve One Step Equations

Example Question #12 : Algebra

Example Question #1 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

All HSPT Math Resources

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