Mathematics
DeweyGambrel
16

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? Percy earns a greater hourly wage of $7.00 at the library. Percy earns a greater hourly wage of $7.00 at the coffee cart. Percy earns a greater hourly wage of $7.50 at the library. Percy earns a greater hourly wage of $7.50 at the coffee cart.

+1
(1) Answers
lilchop06

x = library y = coffee shop Monday: 3x + 2y = 36.50 Tuesday: 2x + 5y = 50 use substitution or elimination. It's easier to use elimination by multiplying the 2nd equation by 1.5. Doing that we get 1.5(2x + 5y = 50) = 3x + 7.5y = 75 So the two equations are now: 3x + 7.5y = 75 3x + 2y = 36.50 Subtract and we have 5.5y = 38.5 y=38.5/5.5 = 7 Now put 7 back into either equation to solve for x 3x + 2y = 36.50 3x+2(7) =36.50 3x+14 =36.50 3x=22.50 X= 22.50/3 = 7.50  He earns 7.50 at the library He earns 7.00 at the coffee cart   Check: 3(7.50) + 2(7) = 36.50 = 22.50 + 14 = 36.50 TRUE 2(7.50) + 5(7) = 50 = 15 +35 = 50 TRUE  He earns a greater hourly wage of 7.50 at the library

Add answer