SOLUTION: Miguel is selling tickets to a barbecue. Adult tickets cost 6.00 and children’s tickets cost 4.00. He sells six ore children’s tickets than adult tickets. The total amount of money

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Miguel is selling tickets to a barbecue. Adult tickets cost 6.00 and children’s tickets cost 4.00. He sells six ore children’s tickets than adult tickets. The total amount of money      Log On


   

Question 1025644: Miguel is selling tickets to a barbecue. Adult tickets cost 6.00 and children’s tickets cost 4.00. He sells six ore children’s tickets than adult tickets. The total amount of money he collects is 184. How many adult tickets and how many children tickets did he sell?
Found 2 solutions by josmiceli, FrankM:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of adult tickets sold
Let +b+ = number of children's tickets sold
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(1) +b+=+a+%2B+6+
(2) +6a+%2B+4b+=+184+
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(2) +3a+%2B+2b+=+92+
and
(1) +-a+%2B+b+=+6+
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Multiply both sides of (1) by +3+
and add the equations
(2) +3a+%2B+2b+=+92+
(1) +-3a+%2B+3b+=+18+
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+5b+=+110+
+b+=+22+
and
(1) +b+=+a+%2B+6+
(1) +22+=+a+%2B+6+
(1) +a+=+16+
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He sold 16 adult tickets and 22 children's tickets
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check:
2) +6a+%2B+4b+=+184+
(2) +6%2A16+%2B+4%2A22+=+184+
(2) +96+%2B+88=+184+
(2) +184+=+184+
OK

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
This can be solved using 2 variables, but I prefer my single variable method.
X= adult tickets sold, X+6 is the number of children tickets.
Next 6X+4(X+6)=184
6X+4X+24=184
10X=160
X=16 X+6=22
16 adults 22 kids , no system of equations.