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 5/2 min. each.
Which statement describes the solution to this inequality?
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The solution to this inequality is that there must be fewer than 12 additional questions for Dennis to complete within the remaining time.
To determine the solution to the inequality, we need to set up the equation based on the information given.
Let x represent the number of remaining questions.
The time spent on the first two questions is 10 minutes, and the rest of the questions will take 5/2 minutes each.
So the total time spent on the remaining questions is (5/2)x.
The total time Dennis has is less than 70 minutes, so the inequality can be written as:
10 + (5/2)x < 70
Now we can solve for x:
Multiply both sides of the inequality by 2 to get rid of the fraction:
20 + 5x < 140
Subtract 20 from both sides:
5x < 120
Divide both sides by 5:
x < 24
Therefore, the solution to the inequality is x is less than 24.
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The inequality that represents the time Dennis has left to spend on the rest of the questions can be written as:
70 - 10 - 10 - (5/2)n > 0
where n represents the number of remaining questions.
To find the solution, we can simplify the inequality:
70 - 20 - (5/2)n > 0
50 - (5/2)n > 0
Now, we can solve this inequality by isolating n:
(5/2)n < 50
n < 10
Therefore, the solution to the inequality is n < 10. This means that Dennis can spend less than 10 minutes on the remaining questions in order to complete his homework within the given time limit.