Question

Lea and danielle are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and strawberry cheesecakes. Lea sold 9 pecan cheesecakes and 8 strawberry cheesecakes for a total of $167. Danielle sold 14 pecan cheesecakes and 11 strawberry cheesecakes for a total of $241. What is the cost each of one pecan cheesecakes and one strawberry cheesecake

Answer 1

pecan cheesecakes =$7

strawberry cheesecake = $13

Explanation:

Hi, to answer this question we have to write a system of equations:

• Lea: 9p +8s =167
• Danielle: 14p +11s= 241

These equations represent the amount sold by each one.

Where p is the number of pecan cheesecakes sold, and s is the number of strawberry cheesecakes sold.

Solving for p in the first equation:

9p =167 -8s

p = (167-8s)/9

p = 167/9 -8/9s

Replacing p in the second equation:

14p +11s= 241

14 ( 167/9 -8/9s) +11s= 241

2338/9 - 112/9s +11s =241

2338/9-241= 112/9s-11s

169/9 =13/9s

169/9 / ( 13/9) = s

$13=s

Replacing s back in the first equation

9p +8s =167

9p+8(13) =167

9p+104 =167

9p =167-104

9p= 63

p=63/9

p= $7