When trying to solve a problem, you may run into a situation with 2 variables. At first you may feel stumped. But just take a breath and ask yourself: “Is this a situation where one of the variables may be redefined by some factor of the other variable?”

What does this mean?

## a situation with 2 variables

Well consider the following problem.

24 vehicles pass by a traffic monitor. Some of the vehicles are motorcycles and some of them are 4 wheeled vehicles.

There were 80 wheels in all.

**How many 4 wheeled vehicles went by?
**

When first thinking this through one realizes that there are 2 variables to this problem.

X is for motorcycle with 2 wheels and Y is for a vehicle with 4 wheels.

2X + 4Y = 80

But are there really 2 variables? In terms of wheels you could say that Y is equal 2x.

y = 2X

2X + 4(2X) = 80

Then solve for X.

2X + 4(2X) = 80

2x + 8x = 80

10X = 80

X = 8

Now since you know Y = 2X, solving for Y is easy.

y = 2X

y = 2(8)

y = 16

By this you cans see that 16 vehicles with 4 wheels went by.

When faced with multiple variables, see if it is possible to redefine variables in terms of another variable.