The cost for 7 dance lessons is 82$. the cost for 11 lessons is 122$. write and solve an equation to find the cost of 4 lessons

$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

16

step-by-step explanation: