percy works two part - time jobs to help pay for college classes. on monday, he works 3 hours at the library…

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.\n3x + 2y = 36.50\n2x + 5y = 50.00\nat which job does percy earn the greater hourly wage? how much does percy earn each hour at this job?\npercy earns a greater hourly wage of $7.00 at the library.\npercy earns a greater hourly wage of $7.00 at the coffee cart.\npercy earns a greater hourly wage of $7.50 at the library.\npercy earns a greater hourly wage of $7.50 at the coffee cart.

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.\n3x + 2y = 36.50\n2x + 5y = 50.00\nat which job does percy earn the greater hourly wage? how much does percy earn each hour at this job?\npercy earns a greater hourly wage of $7.00 at the library.\npercy earns a greater hourly wage of $7.00 at the coffee cart.\npercy earns a greater hourly wage of $7.50 at the library.\npercy earns a greater hourly wage of $7.50 at the coffee cart.

Answer

Explanation:

Step1: Eliminate y to find x

Multiply the first - equation $3x + 2y=36.50$ by 5 and the second - equation $2x + 5y = 50.00$ by 2. The first equation becomes $15x+10y = 182.50$ and the second becomes $4x + 10y=100$. Subtract the second new equation from the first: $(15x + 10y)-(4x + 10y)=182.50 - 100$ $15x+10y - 4x - 10y=82.50$ $11x=82.50$ $x=\frac{82.50}{11}=7.50$

Step2: Substitute x into the first equation to find y

Substitute $x = 7.50$ into $3x + 2y=36.50$. $3\times7.50+2y=36.50$ $22.50+2y=36.50$ $2y=36.50 - 22.50$ $2y = 14$ $y=\frac{14}{2}=7.00$

Answer:

Percy earns a greater hourly wage of $7.50 at the library.