SOLUTION: Tickets to the museum exhibit cost $5.50 for adults and $3 for children. Assume 110 people attended and the museum sold $487.50'worth of tickets. How many adults attended? How many

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Question 938737: Tickets to the museum exhibit cost $5.50 for adults and $3 for children. Assume 110 people attended and the museum sold $487.50'worth of tickets. How many adults attended? How many children attended?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = Number of Adults
Let C = Number of Children
Since we have two unknowns, we need two equations.
Equation 1: A+%2B+C+=+110
Equation 2: 5.5%2AA+%2B+3C+=+487.5
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Solve equation 1 for one of the variables.
Equation 1: A+%2B+C+=+110
A+=+110+-+C
Now plug (110 - C) into equation 2 for A
Equation 2: 5.5%2AA+%2B+3C+=+487.5
5.5%2A%28110+-+C%29+%2B+3C+=+487.5
Multiply the 5.5 through
605+-+5.5C+%2B+3C+=+487.5
Combine like terms.
605+-+2.5C+=+487.5
Subtract 605 from both sides.
-2.5C+=+-117.5
Divide both sides by -2.5
Notice that the two negative signs cancel out.
highlight%28C+=+47%29
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Now Plug 47 in for C and solve for A
A+=+110+-+C
A+=+110+-+%2847%29
highlight_green%28A+=+63%29