Question

Percy works two part-time jobs to help 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.

Answer 1

$3x + 2y = 36.5 \\ 2x + 5y = 50$
$3x + 2y = 36.5 \: \: \: (1)\\ 2x + 5y = 50 (2)\\ 2x = 50 - 5y \\ x = \frac{50 - 5y}{2} \: \: \: \: \: \: \: \: (3) \\ put \: 3 \: into \: 1 \\ 3 \frac{50 - 5y}{2} + 2y = 36.5 \\ \frac{150 - 15y}{2} + 2y = 36.5 \\ 2( \frac{150 - 15y}{2} + 2y) = 2(36.5) \\ 150 - 15y + 4y = 73 \\ 11y = 77 \\ y = 7 \\ 2x + 5(7) = 50 \\ x = 7.5 \\ wage \: working \: in \: coffee \: shop \: is \: higher \: for\: 7.5 \: per \: hour$
the answer is D