Algebra 1, Delta math

Question

Makayla is working two summer jobs, making $19 per hour tutoring and making $12 per hour landscaping. In a given week, she can work no more than 17 total hours and must earn at least $260. If Makayla worked 3 hours landscaping, determine the minimum number of whole hours tutoring that she must work to meet her requirements. If there are no possible solutions, submit an empty answer.

Answer 1

12(3) + 19t ≥ 260

3 + t ≤ 17 ---> t ≤ 14

36 + 19(14) ≥ 260

36 + 266 ≥ 260

302 ≥ 260

Yes, there is a solution.

(260 - 36)/19 = 224/19 = 11.8

36 + 19(11) ≥ 260

36 + 209 ≥ 260

245 ≥ 260

Not true.

36 + 19(12) ≥ 260

36 + 228 ≥ 260

264 ≥ 260

So, she can work a minimum of 12 hours to meet the requirements.

Answer 2

One way to approach this question is to start by calculating how much is earned by working 3 hours at landscaping. Then subtract that amount from $260 which is the minimum that she needs to earn. Next, see if there are enough hours left from the total of 17 max hours to tutor. Figure out how many hours are left and calculate the amount earned by tutoring to see if she can make a total of at least $260