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. (1 point)
Use the elimination method to determine the number of cake slices you can purchase.

Answer 1

Let x be the number of slices of cake and y be the number of slices of pie.

The first equation is: x + y = 100 (since the total number of people at the event is 100)

The second equation is: 3x + 5y = 380 (since each slice of cake costs $3 and each slice of pie costs $5, and the total budget for dessert is $380)

To use the elimination method, we can multiply the first equation by 3 to match the coefficient of x in the second equation:

3(x + y) = 300
3x + 3y = 300

Now, we can subtract this equation from the second equation to eliminate x:

(3x + 5y) - (3x + 3y) = 380 - 300
2y = 80
y = 40

Therefore, you can purchase 40 slices of pie.