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) Responses 3x+5y=100 x+y=380 3 x plus 5 y is equal to 100 x plus y is equal to 380 x+y=100 3x+5y=380 x plus y is equal to 100 3 x plus 5 y is equal to 380 x−3y=380 x+5y=100 x minus 3 y is equal to 380 x plus 5 y is equal to 100 x−y=380 3x−5y=380 x minus y is equal to 380 3 x minus 5 y is equal to 380 Question 2 Use the elimination method to determine the number of cake slices you can purchase. Make sure to show work to receive credit. Upload a picture of your handwritten work.
The correct system of equations to determine the number of slices of cake and pie you can buy is:
x + y = 100 (equation 1)
3x + 5y = 380 (equation 2)
To solve this system of equations using the elimination method, multiply equation 1 by -3:
-3(x + y) = -3(100)
-3x - 3y = -300
Now, add this new equation to equation 2:
-3x - 3y + 3x + 5y = -300 + 380
2y = 80
Divide both sides by 2:
2y/2 = 80/2
y = 40
Substitute the value of y = 40 into equation 1:
x + 40 = 100
x = 100 - 40
x = 60
Therefore, you can purchase 60 slices of cake.