Word problem!! Need variables!

Question

Need variables to write a formula to solve this; I have 66 tires and 27 frames and need to make x two wheel hikes and y three wheel bikes. How many of each can I make to have no wheels or frames left over?

Answer 1

Since you have 27 frames, that's the total number of vehicles you can make. So x + y = 27.

 

Then the number of 2 wheelers can be called 2x, or 2 wheels on x number of vehicles, andthe 3 wheelers can be 3y, or 3 wheels on yh number of vehicles.

 

So your two equations are x + y = 27 and 2x + 3y = 66.

 

Can you solve from there?

Answer 2

Let the number of 2-wheel and 3-wheel bikes be A and B.

A + B = 27  (frames)

The number of wheels required will be:

2A + 3B = 66

Substitution looks easier.

A+B = 27

B = 27-A

Substitute and solve for A

2A + 3B = 66

2A + 3(27-A) = 66

2A + 81 - 3A = 66

-A = -15

A = 15    2-wheelers

 

B = 27 - A

B = 27 - 15

B = 12    3-wheelers