Percy works two part-time jobs to pay for college classes. on monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. on tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. his hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below.
3x + 2y = 36.50
2x + 5y = 50.00
at which job does percy earn the greater hourly wage? how much does percy earn each hour at this job?
a)-percy earns a greater hourly wage of $7.00 at the library.
b)-percy earns a greater hourly wage of $7.00 at the coffee cart.
c)-percy earns a greater hourly wage of $7.50 at the library.
d)-percy earns a greater hourly wage of $7.50 at the coffee cart.

The answer to this question is the letter "C" which is "Percy earns a greater hourly wage of $7.50 at the library". The solution and explanations are to be discussed below:
On Monday, 3 hours at library and 2 hours in the coffee shop 
3x + 2x = 36.5
On Tuesday, 2 hours at library and 5 hours in coffee shop
2x + 5y = 50
We have x to represents the hourly wage in the library
We have y to represents the hourly wage in the coffee shop
Solving for x and y, we have:
3x + 2y = 36.5
3x = 36.5 - 2y
x = (36.5 -2y) /3

2x + 5y=50
2x = 50 -5y
x = (50-5y) /2

Since x = x, we have:
(36.5 -2y) / 3 = (50 - 5y) /2
2 (36.5 -2y) = 3*(50-5y)
73 - 4y = 150 -15y
15y - 4y = 150 - 73
11y = 77
y = 7 (hourly wage for the coffe shop work)

Solving for x, we have:
x = (50 -5y) / 2
x = (50 - 5*7) /2
x = (50 - 35) / 2
x = 15/2
x = 7.5 (hourly wage in the library)

Therefore, the answer is the letter "C".

Main idea on left, details on right