SOLUTION: A group of ten friends purchased tickets to the Miami Dolphins game at a group discount of 20%.Each person paid $55 for each ticket. How much did one friend save by using the group

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Question 1184363: A group of ten friends purchased tickets to the Miami Dolphins game at a group discount of 20%.Each person paid $55 for each ticket. How much did one friend save by using the group discount?
A. $5.50
B. $11.00
C. $13.20
D. $13.75
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


A 20% discount means they paid 80% of the usual price, or 4/5 of the usual price.

So the usual price was 5/4 of what they paid.

So the amount each one saved is the difference between 5/4 of what they paid and what they paid; that difference is 1/4 of what they paid.

1/4 of what each one paid is $13.75. Answer D.

If the informal reasoning is too hard to follow, here is the same solution using formal algebra.

The discounted ticket price was $55.

The discounted price is 80%, or 4/5, of the usual price. If x is the usual price, then

55+=+%284%2F5%29x
x+=+55%2F%284%2F5%29+=+55%2A%285%2F4%29

The amount each friend saved using the group discount is the difference between the usual price and the discounted price, which is

%285%2F4%2955-55+=+%281%2F4%2955+=+55%2F4+=+13.75