Question

Katie works part-time at a Fallbrook riding stable she makes $5 an hour for exercising horses and $10 an hour for cleaning stalls because Katie is full-time student you cannot work more than 12 hours per week she wants to earn no less than 90​

Answer 1

In order to at least earn $90, Katie can work exercising horses for 6 hours and cleaning stalls for 6 hours.

Step-by-step explanation:

Let hours of exercising horses be x --> $5 per hour = 5x

Let hours of cleaning stalls be y --> $10 per hour = 10y

Total earning = $\geq 90$

Total hours = 12

Equation 1:

5x + 10y = $\geq 90$

Equation 2:

x + y $\leq 12$

1. Multiply equation 2 by -5

x + y $\leq 12$ (*-5)

5x + 10y = $\geq 90$

-5x - 5y $\leq -60$

5x + 10y = $\geq 90$

2. Solve

-5x + 5x -5y + 10y = -60 + 90

5y = 30

y = 6

x + y = 12

x + 6 = 12

x = 6

Therefore, in order to at least earn $90, Katie can work exercising horses for 6 hours and cleaning stalls for 6 hours.

Keywords: Simultaneous, hours, equations

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