Question

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.

Answer 1

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.