SOLUTION: While waiting for a friend to decide on a bike to buy for his daughter, Jake looked over the bikes and wagons and, out of boredom, started to count them. He counted 45 vehicles an

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: While waiting for a friend to decide on a bike to buy for his daughter, Jake looked over the bikes and wagons and, out of boredom, started to count them. He counted 45 vehicles an      Log On

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Question 624505: While waiting for a friend to decide on a bike to buy for his daughter, Jake looked
over the bikes and wagons and, out of boredom, started to count them. He counted 45 vehicles and
100 tires but did not bother to keep track of how many vehicles of each type there are. How many
bikes and how many wagons are there? Use linear equations to solve this problem.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the number of wagons
Let +b+ = the number of bikes
given:
(1) +w+%2B+b+=+45+
(2) +4w+%2B+2b+=+100+
------------------
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +4w+%2B+2b+=+100+
(1) +-2w+-+2b+=+-90+
+2w+=+10+
+w=+5+
and, since
(1) +w+%2B+b+=+45+
(1) +5+%2B+b+=+45+
(1) +b+=+40+
There are 40 bikes and 5 wagons
check:
(2) +4%2A5+%2B+2%2A40+=+100+
(2) +20+%2B+80+=+100+
(2) +100+=+100+