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
b) x + y = 100
3x + 5y = 380
Use the elimination method to determine the number of cake slices you purchase? Show your work
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.