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
3x + 5y = 100
x + y = 380
but next you should solve it just to show that you know how.
One way:
y = (380 - x)
so
3 x + 5 (380-x) = 100
3 x + 1900 -5 x = 100
2 x = 1800
x = 900
etc
Let's solve the system of equations:
1) 3x + 5y = 100
2) x + y = 380
First, let's solve equation 2) for y in terms of x:
y = 380 - x
Now, substitute this value of y in equation 1):
3x + 5(380 - x) = 100
Expand this equation:
3x + 1900 - 5x = 100
Combine like terms:
-2x + 1900 = 100
Subtract 1900 from both sides:
-2x = -1800
Divide by -2:
x = 900
Now, substitute this value of x back into equation 2):
900 + y = 380
Subtract 900 from both sides:
y = 380 - 900
y = -520
So, the number of slices of cake (x) that can be bought is 900, and the number of slices of pie (y) that can be bought is -520. However, since we cannot have a negative number of slices, we can conclude that it is not possible to buy -520 slices of pie.
That is pretty funny :)
I apologize for the mistake in my previous response. You were right to point out that the solution I provided was incorrect. Let's solve the system of equations correctly:
1) 3x + 5y = 100
2) x + y = 380
To solve this system, we can use the method of substitution. Let's solve equation 2) for x in terms of y:
x = 380 - y
Now substitute this value of x into equation 1):
3(380 - y) + 5y = 100
Distribute the 3:
1140 - 3y + 5y = 100
Combine like terms:
2y = -1040
Divide by 2:
y = -520
Now substitute this value of y back into equation 2):
x + (-520) = 380
x = 380 + 520
x = 900
So, the number of slices of cake (x) that can be bought is 900, and the number of slices of pie (y) that can be bought is -520. However, since we cannot have a negative number of slices, this solution is not feasible.
I apologize for the confusion. The correct solution is that it is not possible to buy 100 slices of cake and use the entire budget of $380 with the given prices of $3.00 per slice of cake and $5.00 per slice of pie.