SOLUTION: A group of students is planning a trip using cars and minibuses. Each car can hold 5 students and each minibus can hold 14 students. There will be 53 students on the trip. The esti

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A group of students is planning a trip using cars and minibuses. Each car can hold 5 students and each minibus can hold 14 students. There will be 53 students on the trip. The esti      Log On


   

Question 1080464: A group of students is planning a trip using cars and minibuses. Each car can hold 5 students and each minibus can hold 14 students. There will be 53 students on the trip. The estimate for gas costs is $4 for each car and $6 for each minibus. The total cost for gas will be $32. How many cars and how many minibuses will the students use ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of cars used
Let +b+ = the number of minibuses used
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(1) +5a+%2B+14b+=+53+
(2) +4a+%2B+6b+=+32+
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Multiply both sides of (1) by 4
Multiply both sides of (2) by 5
Subtract (2) from (1)
(1) +20a+%2B+56b+=+212+
(2) +-20a+-+30b+=+-160+
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+26b+=+52+
+b+=+2+
and
(2) +4a+%2B+6b+=+32+
(2) +4a+%2B+6%2A2+=+32+
(2) +4a+=+20+
(2) +a+=+5+
Ther are 5 cars and 2 minibuses
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check:
(1) +5a+%2B+14b+=+53+
(1) +5%2A5+%2B+14%2A2+=+53+
(1) +25+%2B+28+=+53+
(1) +53+=+53+
OK
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