
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

Re: Price/Cost Problem
Found the answer:
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
This is the correct answer.
Try the others just for fun.