SOLUTION: Dave sold 40 tickets for a concert. He sold x tickets at $2 each. The rest of the tickets he sold for $3 each. If he collected $88, how much of each type of ticket did he sell?

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Question 1056875: Dave sold 40 tickets for a concert. He sold x tickets at $2 each. The rest of the tickets he sold for $3 each. If he collected $88, how much of each type of ticket did he sell?
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Let
n = number sold at $2 each
k = number sold at $3 each
Two unknowns, so we're looking for two equations
n + k = 40 (Dave sold 40 tickets)
2n + 3k = 88 (He collected $88)
From the top eqn, k = 40-n, substitute this for k in the bottom eqn:
2n + 3(40- n) = 88
2n + 120 - 3n = 88
-n = -32
n = 32 (sold 32 tickets at $2 each)
k = 8 (sold 8 tickets at $3 each)
Check: 8*3 + 32*2 = 24 + 64 = 88 (ok)

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Dave sold 40 tickets for a concert. He sold x tickets at $2 each. The rest of the tickets he sold for $3 each. If he collected $88, how much of each type of ticket did he sell?
Number of $2 tickets sold: x

Number of $3 tickets sold: 40 - x

Cost of $2 tickets: 2x

Cost of $3 tickets: 3(40 - x), or 120 - 3x

We then get the following PROCEEDS equation: 2x + 120 - 3x = 88

2x - 3x = 88 - 120

- x = - 32

x, or number of $2 tickets sold = 

Number of $3 tickets sold: 40 - 32, or  

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