Dennis has less than 70 min. to spend on some homework questions. He spent 10 min. on the first two questions. The rest of the questions will take 52 min. each. Which statement describes the solution to this inequality?

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A. Dennis can complete less than 24 questions.

Step-by-step explanation:

Let x represent the remaining number of questions to be completed.  He can complete each of them in 5/2 minutes each; this gives us the expression 5/2x.

He has already spent 10 minutes; this gives us 5/2x+10.

He has less than 70 minutes to spend; this gives us the inequality

5/2x+10<70

Subtract 10 from each side:

5/2x+10-10 < 70-10

5/2x < 60

Divide both sides by 5/2:

5/2x÷5/2 < 60÷5/2

x < 60/1 ÷ 5/2

To divide fractions, flip the second one and multiply:

x < 60/1 × 2/5

x < 120/5

x < 24

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