SOLUTION: The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 1,486 people enter the fair and $3,479 is collected. How many children and how many

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 1,486 people enter the fair and $3,479 is collected. How many children and how many       Log On


   

Question 1064669: The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 1,486 people enter the fair and $3,479 is collected. How many children and how many adults attended?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of children attended
Let +b+ = number of adults attended
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(1) +a+%2B+b+=+1486+
(2) +1.5a+%2B+4b+=+3479+
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Multiply both sides of (2) by +2+
(2) +3a+%2B+8b+=+6958+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
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(2) +3a+%2B+8b+=+6958+
(1) +-3a+-+3b+=+-4458+
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+5b+=+2500+
+b+=+500+
and
(1) +a+%2B+b+=+1486+
(1) +a+%2B+500+=+1486+
(1) +a+=+986+
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500 adults attended
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check:
(2) +1.5a+%2B+4b+=+3479+
(2) +1.5%2A986+%2B+4%2A500+=+3479+
(2) +1479+%2B+2000+=+3479+
(2) +3479+=+3479+
OK