SOLUTION: A buffet sells plates for seniors at $6, adults at $9, and children for free. If 150 plates were purchased for total receipts of $960 and twice as many adult plates were purcha

Question 702629: A buffet sells plates for seniors at $6, adults at $9, and children for free. If 150 plates were purchased for
total receipts of $960 and twice as many adult plates were purchased as senior plates, how many of each
type of plate were sold?
1) This problem can be solved using a system of equations. Identify the variables to be used in the
system.
2) Write one equation to represent the total number of plates sold.
3) Write one equation to represent the total receipts.
4) Describe how a third equation can be written. What is that equation?
5) Use a system of equations to solve the problem.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A buffet sells plates for seniors at $6, adults at $9, and children for free. If 150 plates were purchased for total receipts of $960 and twice as many adult plates were purchased as senior plates, how many of each type of plate were sold?
1) This problem can be solved using a system of equations. Identify the variables to be used in the system.
2) Write one equation to represent the total number of plates sold.
s + a + c = 150
--------------------------
3) Write one equation to represent the total receipts.
6s + 9a + 0c = 960
--------------------------
4) Describe how a third equation can be written. What is that equation?
a = 2s
-------------
5) Use a system of equations to solve the problem.
Substitute for "a" and solve for "s":
6s + 9(2s) = 960
24s = 960
s = 40 (# of senior plates sold)
----
Substitute for s and a to solve for "c":
s + 2s + c = 150
40 + 80 + c = 150
c = 30 (# of child plates sold)
----
a = 2s = 80 (# of adult plates sold)
========================================
Cheers,
Stan H.
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