Question

1. jessica and daniel are selling cheesecakes for a school fundraiser. customers can buy pecan cheesecakes and apple cheesecakes. jessica sold 7 pecan cheesecakes and 7 apple cheesecakes for a total of $231. daniel sold 10 pecan cheesecakes and 14 apple cheesecakes for a total of $402. what is the cost each of one pecan cheesecake and one apple cheesecake?

pecan apple

Explanation:

Step1: Define variables

Let $x$ = cost of 1 pecan cheesecake, $y$ = cost of 1 apple cheesecake.

Step2: Set up equations

From Jessica's sales: $7x + 7y = 231$
From Daniel's sales: $10x + 14y = 402$

Step3: Simplify first equation

Divide first equation by 7: $x + y = 33$, so $x = 33 - y$

Step4: Substitute into second equation

Substitute $x=33-y$ into $10x + 14y = 402$:
$10(33 - y) + 14y = 402$
$330 - 10y + 14y = 402$
$330 + 4y = 402$

Step5: Solve for y

$4y = 402 - 330 = 72$
$y = \frac{72}{4} = 18$

Step6: Solve for x

Substitute $y=18$ into $x=33-y$:
$x = 33 - 18 = 15$

Answer:

One pecan cheesecake costs $15, and one apple cheesecake costs $18.