Question

5. Carlos and Mike are selling cheesecakes for a school fundraiser. Customers can buy pecan

cheesecakes and apple cheesecakes. Carlos sold 1 pecan cheesecake and 4 apple cheesecakes for a total
of $44. Mike sold 14 pecan cheesecakes and 14 apple cheesecakes for a total of $238. Find the cost
each of one pecan cheesecake and one apple cheesecake.
a. Define variables:
b. System:
c. Solve the systems (optional):

Answer 1

One pecan costs $8. One apple costs $9.

Explanation:

p and a are number of number of pecan and apple sold, respectively.

:::::

"1 pecan cheesecake and 4 apple cheesecakes for $44"

p + 4a = 44

"14 pecan cheesecakes and 14 apple cheesecakes for $238"

14p + 14a = 238

You have a system of two equations in two unknowns:

p + 4a = 44

14p + 14a = 238

:::::

Eliminate the p terms: Multiply the first equation by -14, then add the product to the second equation.

-14p - 56a = -616

 14p + 14a = 238

------------------------

 -42a = -378

a = (-378)/(-42) = 9

p = 44-4a = 8

One pecan costs $8. One apple costs $9.