Jasmine and Jenna are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and apple cheesecakes. Jasmine sold 2 pecan cheesecakes and 8 apple cheesecakes for a total of $146. Jenna sold 4 pecan cheesecakes and 7 apple cheesecakes for a total of $139. find the cost of one pecan cheesecake and the cost of one apple cheesecake
2p+8a = 146
4p+7a = 139
solve for p and a, then find p+a
To find the cost of one pecan cheesecake and the cost of one apple cheesecake, we can set up a system of equations based on the information given.
Let's represent the cost of one pecan cheesecake as "P" and the cost of one apple cheesecake as "A".
From the information given about Jasmine's sales:
2P + 8A = 146 ----(1)
From the information given about Jenna's sales:
4P + 7A = 139 ----(2)
To solve this system of equations, we can use the method of substitution. First, we solve equation (1) for P in terms of A:
2P = 146 - 8A
P = (146 - 8A) / 2
P = 73 - 4A ----(3)
Substituting equation (3) into equation (2):
4(73 - 4A) + 7A = 139
292 - 16A + 7A = 139
-9A = 139 - 292
-9A = -153
A = -153 / -9
A = 17
Now we substitute the value of A back into equation (3) to find P:
P = 73 - 4(17)
P = 73 - 68
P = 5
Therefore, the cost of one pecan cheesecake is $5 and the cost of one apple cheesecake is $17.
To find the cost of one pecan cheesecake and one apple cheesecake, we can set up a system of equations based on the information given.
Let's assume the cost of one pecan cheesecake is represented by "x" dollars, and the cost of one apple cheesecake is represented by "y" dollars.
From the information given, we can set up the following equations:
Equation 1: 2x + 8y = 146 (Jasmine's sales total)
Equation 2: 4x + 7y = 139 (Jenna's sales total)
To solve this system of equations, we have a few options. One method is to use the substitution method:
1. Rearrange Equation 1 to solve for x:
2x = 146 - 8y
x = (146 - 8y) / 2
x = 73 - 4y
2. Substitute the expression for x in Equation 2:
4(73 - 4y) + 7y = 139
Simplify the equation:
292 - 16y + 7y = 139
-9y = 139 - 292
-9y = -153
y = -153 / -9
y = 17
3. Substitute the value of y back into Equation 1 to solve for x:
x = 73 - 4y
x = 73 - 4(17)
x = 73 - 68
x = 5
Therefore, the cost of one pecan cheesecake is $5, and the cost of one apple cheesecake is $17.