Answer:
Hourly wage at the library = x = $7.5
Hourly wage at the coffee cart = y = $7
Step-by-step explanation:
Let
Hourly wage at the library = x
Hourly wage at the coffee cart = y
On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50.
Hence:
3x + 2y = 36.5.... Equation 1
On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50.
2x + 5y = 50...... Equation 2
Combining both Equations
3x + 2y = 36.5.... Equation 1
2x + 5y = 50...... Equation 2
We solve using Elimination method, Multiply Equation 1 by 2 and Equation 2 by 3 which are coefficients of x to eliminate x
6x + 4y = 73 .. Equation 3
6x + 15y = 150...... Equation 4
Subtract Equation 3 from Equation 4
11y = 77
y = 77/11
y = 7
Solving for x using Equation 2
2x + 5y = 50...... Equation 2
2x + 5 × 7 = 50
2x + 35 = 50
2x = 50-35
2x = 15
x = 15/2
x = 7.5
Therefore,
Hourly wage at the library = x = $7.5
Hourly wage at the coffee cart = y = $7
