# Math Help - Price/Cost Problem

1. ## Price/Cost Problem

A certain bakery ran a promotion: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is$2 less than the normal donut price per dozen, what is x?

A 15
B 18
C 21
D 25
E 30

2. ## Re: Price/Cost Problem

P1 is the normal price.
P2 is the promotion price.

X*P1=15 : X purchased at the normal price for $15 (X+3)*P2 = 15 : But you get 3 more, so X+3 times whatever the promotion price is also$15

Now deal with those dozen. A dozen purchased at the promotion price (P2) is \$2 less than a dozen purchased at the normal price (P1):

12P1 - 2 = 12P2

Three equations, three unknowns. Solve it with algebra, or substitute in the different answers to check if they work.

In each case use the given x to solve two of the equations, then check those values in the third equation.

If x=15

(x+3)*P2 = 15 substitute 18P2 = 15 divide P2 = 5/6

12P1 - 2 = 12P2 substitute and add 2 to both sides 12P1 = 10+2 = 12 so P1 = 1

Check with the third equation x*P1=15 substitute 15*1=15