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A toy store sells bicycles and tricycles. It has 60 vehicles for sale. If there are 140 wheels in the store, how many bicycles and how many tricycles are in the store? (Bicycles have 2 wheels and tricycles have 3.)
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20 bicycles and 40 tricycles

Let $a$ and $b$ be the number of bicycles and tricycles in the store respectively. Since there is a total of 60 vehicles we have that $a+b=60 \Longleftrightarrow b=60-a$. The number of wheels is $2 a+3 b$ since each of the $a$ bicycles have two wheels and the $b$ tricycles each have 3 wheels. This gives that $2 a+3 b=140$. Now since $b=60-a$ we have that $2 a+3(60-a)=140 \Longrightarrow a=40$. Then $b=60-40=20$.
by Diamond (78,454 points)

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