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?

Solution Preview

Please see attached file

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 ...

Solution Summary

The solution solves a Word problem in Linear equations.

Graphs and Solving Linear Equations Word Problems (20 Problems). ... Find an equation in slope-intercept form ... Graphs and Solving Linear Equations are investigated. ...

Systems of Linear Equations Word Problem. ... Thank you for using Brainmass. A word problem is solved using systems of linear equations and matrix notation. ...

Systems of Linear Equations Word Problems. ... Let the number of horses sold be x and number of cows sold be y. The equation will be 500x + 300y = 2100 Divide whole ...

... Now read the exact equation in the window at ... Week 3 Discussion Questions-Linear Equations in 2 Variables. 5. a. Write a word problem about grades that explains ...

...linear equations for word problems. The solution is detailed and well presented. Six less than eight times a number (denoted as x) is 8x 6 So the equation...

Word Problems Involving Linear Equations in Two ... Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates ...

... on these discs = 6*4 = 24 Remaining episodes = 86-24 = 62 Equation will be 2x ... The expert examines using systems of linear equations to solve word problems. ...