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

pecan cheesecakes = $7

strawberry cheesecake = $13

Step-by-step 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