Question

Skating school A charges $7 for equipment rental plus $20 per hour for lessons. Skating School B charges $25 for equipment rental plus $12 per hour for lessons. Identify the number of hours for which the equipment rental and fee for lessons is the same for both schools.

Answer 1

Your equations are

20x + 7 = y
12x + 25 = y

Set them equal to each other

20x + 7 = 12x + 25

8x + 7 = 25

8x = 18

X = 18/8 or 2 2/8 or 2 1/4

Answer 2

2.25 hours

Explanation:

Let for x hours the total charges in school A and B are same,

For school A,

Fixed charges = $ 7,

Additional charges per hour = 20

Thus, the total charges for x hours = 7 + 20x

For school B,

Fixed charges = $ 25,

Additional charges per hour = $ 12,

Thus, the total charges for x hours = 25 + 12x

`\implies 7 + 20x = 25 + 12x`

`20x - 12x = 25 - 7`

`8x = 18`

`\implies x = (18)/(8)=2.25\text{ hours}`