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 = [tex]\geq 90[/tex]
Total hours = 12
Equation 1:
5x + 10y = [tex]\geq 90[/tex]
Equation 2:
x + y [tex]\leq 12[/tex]
1. Multiply equation 2 by -5
x + y [tex]\leq 12[/tex] (*-5)
5x + 10y = [tex]\geq 90[/tex]
-5x - 5y [tex]\leq -60[/tex]
5x + 10y = [tex]\geq 90[/tex]
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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