Answer:
<em>Shayla charges $20 per hour for middle school students and $25 per hour for high school students.</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = Shayla's hourly charge for middle school students
y = Shayla's hourly charge for high school students
Last week, Shayla tutored middle school students for 5 hours and high school students for 12 hours. The total earning was 5x+12y. She earned $400 last week, thus:
5x + 12y = 400 [1]
This week, she tutored middle school students for 6 hours and high school students for 10 hours. The total earnings were 6x+10y and it represented $370, thus:
6x + 10y = 370
Dividing by 2:
3x + 5y = 185 [2]
We have formed the system of equations:
5x + 12y = 400 [1]
3x + 5y = 185 [2]
Multiply [1] by -3 and [2] by 5:
-15x - 36y = -1200
15x + 25y = 925
Adding both equations:
-11y = -275
Dividing by -11:
y = -275/(-11) = 25
y = 25
Substituting in [1]:
5x + 12*25 = 400
5x + 300 = 400
5x = 400 - 300 = 100
x = 100/5 = 20
x = 20
Shayla charges $20 per hour for middle school students and $25 per hour for high school students.
