Question

1. norachai and aliyah are selling cheesecakes for a school fundraiser. customers can buy pecan cheesecakes and apple cheesecakes. norachai sold 5 pecan cheesecakes and 1 apple cheesecake for a total of $79. aliyah sold 5 pecan cheesecakes and 2 apple cheesecakes for a total of $93. what is the cost each of one pecan cheesecake and one apple cheesecake? a) pecan cheesecake: $10, apple cheesecake: $19 b) pecan cheesecake: $7, apple cheesecake: $7 c) pecan cheesecake: $14, apple cheesecake: $13 d) pecan cheesecake: $7, apple cheesecake: $9 e) pecan cheesecake: $13, apple cheesecake: $14

Explanation:

Step1: Define variables

Let \( p \) be the cost of one pecan cheesecake and \( a \) be the cost of one apple cheesecake.

Step2: Set up equations

From Norachai's sales: \( 5p + a = 79 \)
From Aliyah's sales: \( 5p + 2a = 93 \)

Step3: Subtract the first equation from the second

\( (5p + 2a) - (5p + a) = 93 - 79 \)
\( 5p + 2a - 5p - a = 14 \)
\( a = 14 \)

Step4: Substitute \( a = 14 \) into the first equation

\( 5p + 14 = 79 \)
\( 5p = 79 - 14 \)
\( 5p = 65 \)
\( p = \frac{65}{5} = 13 \)

Answer:

E) pecan cheesecake: $13, apple cheesecake: $14