You are planning an event for 100 people. You have a budget of $380.00 for dessert. Each slice of cake costs $3.00 and each slice of pie costs $5.00. Select from below the system of equations to determine the number of slice of cake and pie you can buy. Part 2 Use the elimination method to determine the number of cake slices you can purchase
Let's assume the number of cake slices as x and the number of pie slices as y.
According to the given information,
Each slice of cake costs $3.00, so the cost of x cake slices would be 3x dollars.
Each slice of pie costs $5.00, so the cost of y pie slices would be 5y dollars.
We know that the total budget for dessert is $380.00, so the equation representing the total cost is:
3x + 5y = 380 (Equation 1)
We also know that the total number of people attending the event is 100. So, the equation representing the total number of slices is:
x + y = 100 (Equation 2)
Using the elimination method, let's solve the above system of equations to determine the number of cake slices (x) you can purchase:
Multiply Equation 2 by -3 on both sides:
-3(x + y) = -3(100)
-3x - 3y = -300 (Equation 3)
Add Equation 3 to Equation 1:
(3x + 5y) + (-3x - 3y) = 380 + (-300)
2y = 80
Divide by 2 on both sides:
y = 40
Substitute y = 40 into Equation 2:
x + 40 = 100
x = 100 - 40
x = 60
Therefore, you can buy 60 slices of cake.