Let's assume the number of slices of cake as "c" and the number of slices of pie as "p".
According to the given information, the budget for desserts is $380. We can form the equation:
3c + 5p = 380
We also know that the total number of people attending the event is 100. So, the total number of dessert slices will be 100. We can form the equation:
c + p = 100
Now, we can use the elimination method to determine the number of cake slices we can purchase.
First, let's multiply the second equation by 3 to make the coefficients of "c" in both equations the same:
3c + 3p = 300
Now, we can subtract the first equation from the new equation to eliminate the variable "c":
(3c + 3p) - (3c + 5p) = 300 - 380
3c - 3c + 3p - 5p = -80
-2p = -80
Dividing both sides by -2, we get:
p = 40
Therefore, we can buy 40 slices of pie. To find the number of slices of cake, we can substitute this value of p back into one of the original equations (let's use the second equation):
c + p = 100
c + 40 = 100
c = 100 - 40
c = 60
Therefore, we can buy 60 slices of cake.
So, we can buy 60 slices of cake and 40 slices of pie within a budget of $380.
You are planning an event for 100 people you have a budget of $380 per dessert. Each slice of cake cost three dollars and each slice of pie cost five dollars write a system of equations to determine the number of slices of cake and pie you can buy.
Use the elimination method to determine the number of cake slices you can purchase
1 answer