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
x+y=100
3x+5y=380
x plus y is equal to 100 3 x plus 5 y is equal to 380
3x+5y=100
x+y=380
3 x plus 5 y is equal to 100 x plus y is equal to 380
x−y=380
3x−5y=380
x minus y is equal to 380 3 x minus 5 y is equal to 380
x−3y=380
x+5y=100
x minus 3y is equal to 380 x plus 5y is equal to 100
Use the elimination method to determine the number of cake slices you can purchase.
To use the elimination method, we will multiply the first equation by 3 and the second equation by -1, then add the two equations together to eliminate the variable x.
(3)(x minus 3y) = (3)(380)
-1(x plus 5y) = -1(100)
This simplifies to:
3x minus 9y = 1140
-x minus 5y = -100
Adding the two equations together, we get:
2x - 14y = 1040
To solve for x, we divide by 2:
x - 7y = 520
Now we have a system of equations:
x - 7y = 520
3x + 5y = 380
We can now solve this system of equations to find the number of cake slices we can purchase.
I don't think that is correct. Is there any other way to solve this?
Apologies for the incorrect approach earlier. Yes, we can also solve this problem using the substitution method. Let's rewrite the system of equations:
x + y = 100 (1)
3x + 5y = 380 (2)
From equation (1), we can write x = 100 - y. Now, substitute this value of x in equation (2):
3(100 - y) + 5y = 380
300 - 3y + 5y = 380
2y = 80
y = 40
Now, substitute the value of y back in equation (1) to find x:
x + 40 = 100
x = 100 - 40
x = 60
Therefore, you can buy 60 slices of cake (x) and 40 slices of pie (y) within your budget of $380.