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HSPT Math : How to solve two-step equations

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #3 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

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.

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Example Question #4 : 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 #83 : How To Solve Two Step Equations

A parking garage charges a minimum fee of $\$7$ to park in the garage. It also charges an additional fee of $\$2$ for every hour, or portion of an hour, in which a person parks in the garage. Cliff wants to pay a maximum of $\$20$ to park there. If he pulls into the garage at exactly $7\textup{:}00\textup { AM}$ , when must he leave at latest?

Possible Answers:

$1\textup{:}00\textup { PM}$

$12\textup{:}30\textup { PM}$

$1\textup{:}30\textup { PM}$

$2\textup{:}30\textup { PM}$

Correct answer:

$1\textup{:}00\textup { PM}$

Explanation:

Let be the number of hours that Cliff parks his car in the garage. Since he pays a flat fee of $\$7$ plus $\$2$ per hour or portion thereof, he pays 2X + 7 dollars. Since he does not want to spend more than $\$20$ ,

$2X + 7 \leq 20$

$2X + 7 - 7 \leq 20 - 7$

$2X \leq 13$

$2X \div 2 \leq 13 \div 2$

$X \leq 6.5$

Since a portion of an hour counts as much as an hour, must be a whole number.

$X \leq 6.5$

implies that

$X \leq 6$ .

Cliff can park in the garage for a maximum of 6 hours, and since he entered the garage at $7:00\textup { AM}$ , he must exit hours later:

7+ 6 - 12 = 1 ,

or $1:00\textup { PM}$ .

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Example Question #61 : Operations & Algebraic Thinking

Solve the following:

$(12+13)\times2$

Possible Answers:

Correct answer:

Explanation:

$(12+13)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

12+13=25

$25\times2=50$

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Example Question #21 : Orders Of Operations

Solve:

$(34+17)\times2$

Possible Answers:

102

Correct answer:

102

Explanation:

$(34+17)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

34+17=51

$51\times2=102$

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HSPT Math : How to solve two-step equations

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #3 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

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

Example Question #83 : How To Solve Two Step Equations

Example Question #61 : Operations & Algebraic Thinking

Example Question #21 : Orders Of Operations

All HSPT Math Resources

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