Jane and Jeff are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and strawberry cheesecakes. Jane sold 14 New York Style Cheesecakes and 4 Strawberry cheesecakes for a total of $250. Jeff sold 7 New York Style cheesecakes and 4strawberry cheesecakes for a total of $170. What is the cost of each of one New York Style cheesecake and one Strawberry Cheesecake?
if the prices are n and s, then we have
14n + 4s = 250
7n + 4s = 170
now just find c and s.
Just looking at the numbers, I suspect a typo, but go with what you have written.
To solve this problem, we need to set up a system of equations. Let's say the cost of one New York Style cheesecake is "x" dollars, and the cost of one Strawberry cheesecake is "y" dollars.
From the information given, we can create the following equations:
Equation 1: 14x + 4y = 250 (as Jane sold 14 New York Style cheesecakes and 4 Strawberry cheesecakes for a total of $250)
Equation 2: 7x + 4y = 170 (as Jeff sold 7 New York Style cheesecakes and 4 Strawberry cheesecakes for a total of $170)
Now, we can solve this system of equations to find the values of "x" and "y."
There are several methods to solve a system of equations, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.
From Equation 2, solve it for x:
7x + 4y = 170
7x = 170 - 4y
x = (170 - 4y) / 7
Substitute this expression for "x" into Equation 1:
14x + 4y = 250
14 * [(170 - 4y) / 7] + 4y = 250
Divide both sides of the equation by 2 to simplify it:
[(170 - 4y) / 7] + (2y/7) = 125/7
Multiply both sides of the equation by 7 to eliminate the fractions:
170 - 4y + 2y = 125
Combine like terms:
-2y = -45
Solve for "y":
y = -45 / -2
y = 22.5
Now that we have the value of "y," we can substitute it back into Equation 2 to find the value of "x":
7x + 4(22.5) = 170
7x + 90 = 170
7x = 170 - 90
7x = 80
Solve for "x":
x = 80 / 7
x = 11.43 (rounded to two decimal places)
Therefore, the cost of one New York Style cheesecake is approximately $11.43, and the cost of one Strawberry cheesecake is approximately $22.50.