Question

Solve the word problem below by creating and solving a system of equations by elimination:

"Shayla tutors middle school students and high school students. She charges a different rate for each. Last week, she tutored middle school students for 5 hours and high school students for 12 hours. This week, she tutored middle school students for 6 hours and high school students for 10 hours. She earned $400 last week and $370 this week. How much does she charge each."

Answer 1

Shayla charges $20 per hour for tutoring middle school students and $25 per hour for tutoring high school students.

Step-by-step explanation:

To solve this word problem, let us first define two variables: let x be the rate Shayla charges per hour for tutoring middle school students, and let y be the rate she charges per hour for high school students. We can create two equations based on the information provided:

1. 5x + 12y = 400 (Last week's earnings)
2. 6x + 10y = 370 (This week's earnings)

We will use the elimination method to solve this system of equations. To eliminate one variable, we can multiply the first equation by 6 and the second equation by 5:

• (5x + 12y) × 6 = 400 × 6
• (6x + 10y) × 5 = 370 × 5

Simplifying gives us:

• 30x + 72y = 2400
• 30x + 50y = 1850

Now subtract the second equation from the first:

• (30x + 72y) - (30x + 50y) = 2400 - 1850
• 22y = 550
• y = 25

With the value of y found, we can substitute it back into one of the original equations:

• 5x + 12(×25) = 400
• 5x + 300 = 400
• 5x = 100
• x = 20

So, Shayla charges $20 per hour for tutoring middle school students and $25 per hour for tutoring high school students.