Gabby is working over the summer to save money for college. She earns $15 per hour working at a coffee shop and $12 per hour working at a gym. She can work at most 40 hours per week and needs to earn at least $500 per week.

Question

Given Gabby's constraints, which pairs (c,g) represent possible numbers of hours she could work at the coffee shop, c, and at the gym, g?

Questions
(12,24), (16,16), (20,20) (8,32)

Answer 1

To determine which pairs (c,g) are possible given Gabby's constraints, we need to consider the following:
1. She can work at most 40 hours per week.
2. She needs to earn at least $500 per week.

Let's start by calculating the earnings for each pair (c,g):
Earnings from the coffee shop (Ec) = $15 * c
Earnings from the gym (Eg) = $12 * g

Now we can calculate the total earnings (Et) for each pair:
Et = Ec + Eg

Let's consider each pair:

1. (12,24):
Ec = $15 * 12 = $180
Eg = $12 * 24 = $288
Et = $180 + $288 = $468 (less than $500)

This pair is not possible.

2. (16,16):
Ec = $15 * 16 = $240
Eg = $12 * 16 = $192
Et = $240 + $192 = $432 (less than $500)

This pair is not possible.

3. (20,20):
Ec = $15 * 20 = $300
Eg = $12 * 20 = $240
Et = $300 + $240 = $540 (meets the minimum requirement of $500)

This pair is possible.

4. (8,32):
Ec = $15 * 8 = $120
Eg = $12 * 32 = $384
Et = $120 + $384 = $504 (meets the minimum requirement of $500)

This pair is possible.

Therefore, the pairs (20,20) and (8,32) represent possible numbers of hours Gabby could work at the coffee shop and at the gym, given her constraints.