Question

8) Lisa and Jasmine are selling cheesecakes for a school fundraiser. Customers can buy pecan

cheesecakes and apple cheesecakes. Lisa sold 3 pecan cheesecakes and 7 apple cheesecakes for a
total of $130. Jasmine sold 12 pecan cheesecakes and 14 apple cheesecakes for a total of $338.
Find the cost each of one pecan cheesecake and one apple cheesecake.

Answer 1

9514 1404 393

Answer:

both cost $13 each

Explanation:

Let p and a represent the costs of pecan and apple cheesecakes, respectively.

3p +7a = 130 . . . . . . Lisa's sale

12p +14a = 338 . . . . Jasmine's sale

Both the ratios of p-coefficients (4) and a-coefficients (2) are "nice" numbers, so "elimination" is a viable solution method here.

Subtracting twice the first equation from the second eliminates 'a'.

(12p +14a) -2(3p +7a) = (338) -2(130)

6p = 78 . . . . . simplify

p = 13 . . . . . . .divide by 6

Substituting into the first equation gives ...

3(13) +7a = 130

7a = 91 . . . . . . . subtract 39

a = 13 . . . . . . . . divide by 7

The cost of one pecan cheesecake is $13; the cost of one apple cheesecake is $13.

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A graphing calculator can solve the two equations nicely. Below is a graph of them, showing the solution is (p, a) = (13, 13). Graphing calculators and some scientific calculators can also solve these equations when they are written in matrix or augmented matrix form. It can be worthwhile to learn how to use these calculator features.