Question

Chelsea and Aubree are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. Chelsea sold 5 pecan cheesecakes, , and 3 chocolate marble cheesecakes, , for a total of $160. Aubree sold 5 pecan cheesecakes and 10 chocolate marble cheesecakes for a total of $300. Write equations to represent the scenario. Then, find the cost each of one pecan cheesecake and one chocolate marble cheesecake.

Answer 1

Chelsea sold:

$5p+3c=160$

Aubree sold:

$5p+10c=300$

Subtracting the first equation from the second equation, it follows that:

$\begin{gathered} 7c=140 \\ c=20 \end{gathered}$

Substitute x=20 into the first equation:

$\begin{gathered} 5p+3(20)=160 \\ 5p=100 \\ p=20^{\circ} \end{gathered}$

Cheese: 5p + 3c = 160

Aubree: 5p + 10c = 300

Pecan Cheesecake: $ 20

Chocolate Marble Cheesecake: $ 20