Inspection fee plus $22 per hour. A customer with a coupon for 40% off the inspection fee pays $124 for a 4-hour repair. How many hours are worked when a customer pays $126 without a coupon?

Answer 1

In problems like this, especially if on a timed test, you want to zero in on the answer being sought. Here it's the number of repair hours when there's no discount on the inspection fee. So the basic math sentence is:

Fee plus (X repair hours times $22 an hour) equals $126.

If we knew the fee, we could solve for X. The beginning of the problem provides the way, It gives an example of $124 spent for 4 repair hours when 40 percent of the fee was not charged. If we think of the total fee as 100 percent, then 60 percent of this fee was charged. So our equation is:

.6f + 4(22) = 124 or .6f = 124 - 88 = 36 or fee = $60

Back to our first equation, which becomes:

60 + 22X = 126 or 22X = 66 or X = 3 hours . . . and we're done!

Answer 2

Hi Brooke S.,

For the inspection fee (which is unknown, lets call it x), the customer has a 40% off coupon. So .40*x is equal to the discount amount of the inspection fee but we need to know the amount paid which is .60*x.

The inspection fee plus $22/hr times the hrs worked is equal to the total cost. We know the total cost of $124 and we know the time for the repair, 4 hrs. Lets write an equation.

.60*x + $22/hr *(4 hrs) = $124

.60*x + $88 = $124

.60*x = $36

x = $60, this is the cost of the inspection fee.

Now that we know the cost of the inspection fee, we can find the hours worked for the second part of the problem.

The customer pays the inspection fee plus $22 times the hours worked (lets call this y) equals the cost of the repair, $126.

$60 + $22*y = $126

$22*y = $66

y = 3 hrs, answer to the problem, the hours worked.

I hope this helps, Joe.