Answer:
$70 for 4 lessons
Step-by-step explanation:
Represent the cost of one dance lesson by d.
Assume that there is an upfront charge of c.
Then the total cost formula is
c(x) = c + dx
In the first case, we have: 82 = c + d(7), and
in the second case, we have 122 = c + 11d
Solving the first equation for c, we get: c = 82 - 7d.
Substituting this result into the second equation:
122 = (82 - 7d) + 11d, or
40 = 4d, or d = 4. Each lesson costs $4.
Since 82 = c + d(7), subbing 4 for d yields
82 = c + 28, which in turn yields c = 54. The upfront charge is $54.
Thus, the governing equation is c(x) = $54 + ($4/lesson)x, where c(x) represents the total cost and x the number of dance lessons.
The cost of 4 lessons is then:
c(4) = $54 + ($4/lesson)(4 lessons) = $54 + $16 = $70
The cost of 4 lessons, including the upfront charge, is $70
