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? 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.

Answer 1

To solve the system, the best way to do it is by eliminatiion.  Multiply the first equation by -2 and the second equation by 3.  This changes the system to -6x-4y= -73 and 6x+15y= 150.  When you add those together, the x's are eliminated, leaving 11y = 77 and y = 7.  Sub that in to any one of the above equations to solve for x.  6x + 15(77) = 150 and 6x + 105 = 150.  6x = 45 and x=7.5.  If x is the library and y is the coffee cart, then he makes more at the library.  Your choices aren't numbered, but it's the third one.