Question

Greg wants to earn at least $35 trimming trees. He charges $6 per hour and pays $7 in equipment fees. What are the possible numbers of hours Greg could trim trees? Use t for the number of hours.

a) t ≥ 6 hours
b) t ≥ 7 hours
c) t ≥ 8 hours
d) t ≥ 9 hours

Answer 1

Greg must work at least 7 hours to earn a minimum of $35 after paying a $7 equipment fee. We set up an inequality to find the least number of hours (t) needed, solving for t ≥ 7.

Step-by-step explanation:

The question revolves around determining how many hours Greg needs to work trimming trees to earn at least $35, considering he charges $6 per hour and has a fixed equipment fee of $7. To find the solution, we must set up an inequality that takes into account his hourly rate, his goal earnings, and the equipment fee.

Let t represent the number of hours Greg works. The equation for Greg's earnings, E, after paying the equipment fee is:
E = 6t - 7

To meet his goal, Greg's earnings must be at least $35, expressed with the following inequality:
E ≥ 35
Substituting the earnings equation into the inequality gives us:
6t - 7 ≥ 35

To find the value of t, we add 7 to both sides and then divide by 6, resulting in:
t ≥ 7

Conclusion

Therefore, the possible number of hours Greg could trim trees to earn at least $35 is at least 7 hours, which corresponds to option b.