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.

Answer 1

Hourly wage at the library = x = $7.5

Hourly wage at the coffee cart = y = $7

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