Answer:the initial cost that Mrs. Barefoot must pay for the dance lessons is $10
22 lessons cost $252
Explanation:
Let x represent the initial cost that Mrs. Barefoot must pay for the dance lessons.
Let y represent the cost of each lesson.
Mrs. Barefoot signs her daughter up for dance lessons. She pays $120 for ten lessons. This means that
x + 10y = 120 - - - - - - - - - -1
She also pays $65 for five lessons. This means that
x + 5y = 65
Substituting x = 65 - 5y into equation 1, it becomes
65 - 5y + 10y = 120
- 5y + 10y = 120 - 65
5y = 55
y = 55/5 = 11
Substituting y = 11 into x = 65 - 5y , it becomes
x = 65 - 5 × 11
x = 65 - 55
x = 10
The cost of 22 lessons would be
10 + 22 × 11 = $252