Question

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.
a) 3x + 5y = 100
x + y = 380

b) x + y = 100
3x + 5y = 380

c) x - 3y = 380
x - 5y = 100

d) x - y = 380
3x - 5y = 380

Answer 1

Use the elimination method to determine the number of cake slices you purchase? Show your work

Answer 2

b) x + y = 100
3x + 5y = 380

Answer 3

To solve the system of equations using the elimination method, we'll eliminate one variable by multiplying one of the equations by a suitable constant and then adding or subtracting the equations.

First, let's multiply the first equation by 3:

3(x + y) = 3(100)
3x + 3y = 300

Now we have:

3x + 3y = 300
3x + 5y = 380

Next, subtract the first equation from the second equation:

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

Now, divide both sides by 2 to solve for y:

2y/2 = 80/2
y = 40

So, the number of pie slices you purchase is 40.