SOLUTION: At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. Y

Question 121544: At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. You need to know that to prepare the correct amount of food and for future planning. Each adult dinner cost $6 and each child's dinner cost $3.50.
Let a = number of adult dinners
Let c = number of child dinners

1. Write two equations to represent the total amount raised from the dinner and the total
Use substitution to solve the above system of equations. How many adult dinners were sold and how many child dinners were sold?
I would like to know of how do i solve this problem??

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Well this uses a system of equations so lets first come up with that system.

Since its $6 per adult meal and $3.50 per child meal and you made $935 the first equation is:

6a+3.50c=935

to make the math a little easier I would multiply that by 100 to clear the decimal but you don't have to, either way it works out.

600a + 350c = 93500

Since 210 meals served to children and adults combined the second equation is:

a + c = 210.

so your system of equations is now:

600a + 350c = 93500
a + c = 210

now we start solving using substitution. First solve equation one for a.

a = 210-c

now substitute that into equation on and solve for c.

600a + 350c = 93500 --> substitute a = 210-c in for a
600(210-c) + 350c = 93500 --> Multiply
126000 - 600c + 350c = 93500 --> Combine like terms
126000 - 250c = 93500 --> Subtract 126000 from both sides
-250c = -32500 --> divide both sides by -250
c = 130

now that we have a value for c go back and solve for a.

a = 210-130 = 80

so now we know that there were 80 adults served and 130 children served at the banquet.
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