Question

David wants to earn more than $46 trimming trees. He charges $6 per hour and pays $8 in equipment fees. What are the possible numbers of hours David could trim trees? Use t for the number of hours. Write your answer as an inequality solved for .

Answer 1

David needs to work more than 9 hours to earn over $46, considering he charges $6 per hour and has an equipment fee of $8. The inequality expressing this is 6t - 8 > 46, which solves to t > 9.

Step-by-step explanation:

David wants to earn more than $46 trimming trees. He charges $6 per hour for his service and has a fixed equipment fee of $8. To find the possible numbers of hours, let's represent the number of hours by t and set up an inequality. The total earnings for t hours will be the hourly rate multiplied by t minus the equipment fees. So, the inequality showing David’s desired earnings is:

6t - 8 > 46

To solve for t, we need to isolate it on one side of the inequality:

6t > 46 + 8

6t > 54

Divide both sides by 6 to get:

t > 9

This means David needs to work more than 9 hours to earn more than $46.