9) norachai and aliyah are selling cheesecakes for a school fundraiser. customers can buy pecan cheesecakes…

9) 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

9) 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

Answer

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