SOLUTION: The entrance fee for visiting a museum is $76 for 4 children and 4 adults. The entrance fee for 6 children and 3 adults is $75. Find the total cost of visiting the museum for a fam

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The entrance fee for visiting a museum is $76 for 4 children and 4 adults. The entrance fee for 6 children and 3 adults is $75. Find the total cost of visiting the museum for a fam      Log On


   

Question 1064749: The entrance fee for visiting a museum is $76 for 4 children and 4 adults. The entrance fee for 6 children and 3 adults is $75. Find the total cost of visiting the museum for a family of 5 adults and 3 children.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to find the cost for ONE adult and
ONE child to visit
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Let +a+ = the cost for one adult
Let +b+ = the cost for one child
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(1) +4a+%2B+4b+=+76+
(2) +3a+%2B+6b+=+75+
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(1) +2a+%2B+2b+=+38+
(1) +a+%2B+b+=+19+
and
(2) +a+%2B+2b+=+25+
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Subtract (1) from (2)
(2) +a+%2B+2b+=+25+
(1) +-a+-+b+=+-19+
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+b+=+6+
and
(1) +a+%2B+b+=+19+
(1) +a+%2B+6+=+19+
(1) +a+=+13+
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+5a+=+5%2A13+
+5a+=+65+
and
+3b+=+3%2A6+
+3b+=+18+
and
+5a+%2B+3b+=+65+%2B+18+
+5a+%2B+3b+=+83+
The cost for a family of 5 adults and 3 children
is $83
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check my math