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?

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?

Mercury · Answer

it wants to know which hourly wage (either x or y) is higher, so you'll need to solve the system of equations for x and y

as a hint, you can multiply the first equation by 2, and the second equation by 3. you'll end up with 6x in both equations, which means you can subtract the two equations to eliminate all x terms. then it's easy to solve for y. you can then plug that y-value back into either equation to solve for x.

once you have your x and y value, simply report which one is higher, and what the value is