You are planning an event for 100 people. You have a budget of $380 for dessert. Each slice of cake costs $3.00 and each slice of pie costs $5.00.
Write a system of equations to determine the number of slices of cake and pie you can buy.
x+y=100
3x+5y=380
x−3y=380
x+5y=100
3x+5y=100
x+y=380
x−y=380
3x−5y=380
Use the elimination method to determine the number of cake slices you can purchase.
Make sure to show work to receive credit.
To use the elimination method, we need to eliminate the x variable in one of the equations by multiplying one of the equations by a constant and adding or subtracting it from the other equation.
Let's use the first equation x + y = 100 and multiply it by -3 to get -3x - 3y = -300:
-3x - 3y = -300
3x + 5y = 380
Adding these two equations together, we eliminate the x variable:
(3x + 5y) + (-3x - 3y) = 380 + (-300)
2y = 80
y = 40
Now, substitute this value for y into one of the original equations to solve for x. Let's use the first equation x + y = 100:
x + 40 = 100
x = 60
Therefore, you can purchase 60 slices of cake.