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.
From Norachai's sales: \( 5p + a = 79 \) (Equation 1)
From Aliyah's sales: \( 5p + 2a = 93 \) (Equation 2)

Step2: Subtract Equation 1 from Equation 2

\( (5p + 2a) - (5p + a) = 93 - 79 \)
Simplify: \( 5p + 2a - 5p - a = 14 \)
So, \( a = 14 \)

Step3: Substitute \( a = 14 \) into Equation 1

\( 5p + 14 = 79 \)
Subtract 14 from both sides: \( 5p = 79 - 14 = 65 \)
Divide by 5: \( p = \frac{65}{5} = 13 \) Wait, no, wait. Wait, let's check the options. Wait, maybe I made a mistake. Wait, let's check the options again. Wait, the options have E as pecan:13, apple:14. Wait, let's re - calculate.

Wait, Equation 1: \( 5p + a = 79 \)
Equation 2: \( 5p + 2a = 93 \)
Subtract Equation 1 from Equation 2: \( (5p + 2a)-(5p + a)=93 - 79\)
\( 5p+2a - 5p - a=14\)
\( a = 14 \)
Then plug \( a = 14 \) into Equation 1: \( 5p+14 = 79\)
\( 5p=79 - 14=65\)
\( p = 13 \)
So pecan is $13, apple is $14, which is option E.

Answer:

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