Question

Ryan wants to earn at least $48 trimming trees. He charges $7 per hour and pays $8 in equipment fees. What are the possible numbers of hours Ryan could trim trees? Use t for the number of hours. Write your answer as an inequality solved for t .

Answer 1

To determine the possible numbers of hours (t) that Ryan could trim trees in order to earn at least $48, we can set up an inequality based on the given information.

Ryan earns $7 per hour and has to pay $8 in equipment fees. So, for each hour of work, he earns $7 - $8 = -$1 (negative $1) because he has to subtract the equipment fees.

Now, let's set up the inequality to find the minimum number of hours (t) required:

Ryan wants to earn at least $48, so we can write:

7t - 8t ≥ 48

Now, combine like terms on the left side:

-1t ≥ 48

Since we want to solve for t, we need to isolate t by dividing both sides of the inequality by -1. When you divide by a negative number, remember to reverse the direction of the inequality:

t ≤ -48

So, the inequality solved for t is:

t ≤ -48

However, it doesn't make sense to have a negative number of hours, so the number of hours Ryan could trim trees must be greater than or equal to 0:

t ≥ 0

In conclusion, Ryan could trim trees for 0 hours or any positive number of hours to earn at least $48.

Answer 2

to find the possible numbers of hours ryan could trim trees and earn at least $48, you can set up the following inequality:

7t - 8 ≥ 48

now, solve for 't':

7t ≥ 48 + 8
7t ≥ 56

divide both sides by 7:

t ≥ 8

so, ryan must work at least 8 hours to earn at least $48 by trimming trees.