# Linear equations: Word problem

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Bill runs Bill's Big Bikes, a company that manufactures bicycles and specialty adult-sized tricycles. The bicycles and tricycles use the same-sized wheels and identical seats. Right now, Bill has 68 wheels in the shop and needs to order seats. Unfortunately, the company that supplies the seats will only ship seats in boxes of 6. Bill does not want to order more wheels and does not want to order more seats than he needs.

How many bicycles and tricycles should be manufactured to use all of the wheels Bill has in stock and all of the seats that he will ultimately order? How many boxes of seats will he order?

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The solution solves a Word problem in Linear equations.

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Let the number of bicycles be x

Let the number of tricycles be y

Each bicycle uses 2 wheels and each tricycle uses 3 wheels

no of wheels available= 68

Therefore since no more wheels are to be ordered

2 x + 3 y <= 68 ---------------(1)

Each bicycle and each tricycle uses 1 seat

Since seats are only shipped in boxes of 6

Let z be the no of boxes of seats ordered

Therefore no of seats ordered= 6 z

Since only that number of seats are to be ordered as are actually required

x+y=6z ------------------(2)

Therefore the equations are:

2 x + 3 y <= 68 ---------------(1)

x+y=6z ------------------(2)

We will first solve the equations graphically

We will draw a number of lines corresponding to z=1,2,3,4,5,6,7

in the equation x+y=6z ------------------(2)

And we will draw a graph for equation 2 x + 3 y = 68 ...

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