HSPT Math : How to solve one-step equations

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #1 : How To Solve One Step Equations

Solve for  : 

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Solve One Step Equations

In a math contest, the team from Lincoln High comprised five students - Melanie, Ned, Olivia, Phyllis, and Quinn. Melanie outscored Ned by 12 points; Ned outscored Quinn by 19 points; Phyllis outscored Ned by 45 points and Olivia by 20 points. Who came in third among the five?

Possible Answers:

Quinn

Melanie

Ned

Phyllis

Olivia

Correct answer:

Melanie

Explanation:

Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:

Phyllis, Olivia, Melanie, Ned, Quinn

Melanie scored third among the five.

Example Question #2 : How To Solve One Step Equations

Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?

Possible Answers:

Correct answer:

Explanation:

Divide .

Answer: Jasmine has completed 80% of the race.

Example Question #2 : 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

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

Example Question #2 : 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:

20 dollars

60 dollars

22 dollars

30 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. 

Example Question #4 : How To Solve One Step Equations

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:

Bailey

Cara

There is not enough information to solve this problem.

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.

Example Question #6 : How To Solve One Step Equations

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:

3 pounds of apples and 2 pounds of bananas

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

1.5 pounds of oranges and 4 pounds of bananas

2 pounds of oranges and 1 pound of apples

1 pound of oranges, 1.5 pounds of apples and 1.5 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 * (# Apples)

Example Question #7 : How To Solve One Step Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

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

Example Question #8 : How To Solve One Step Equations

Solve for :   

Possible Answers:

Correct answer:

Explanation:

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

Example Question #3 : How To Solve One Step Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

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

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