# ISEE Upper Level Math : Variables

## Example Questions

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### Example Question #1 : How To Multiply Variables

Machine A can produce 4 buttons in 2 days.  Machine B can produce 20 buttons in 4 days.  How many buttons can Machine A and B, working together, produce in 40 days?

Explanation:

First determine how many buttons each machine can produce in a day.

Machine A:

Machine B:

Machine A and B can produce 7 buttons per day when they are working together.

### Example Question #1 : Operations

Brian has 3 siblings.  When his family orders pizza, each of the 4 children is given of the pizza.  Brian does not feel well so he only finishes of his pizza.  If the original pizza consisted of 12 slices of pizza, how many slices did Brian eat?

Explanation:

Brian eats .

So Brian eats

Solve for :

Explanation:

### Example Question #4 : How To Multiply Variables

Simplify:

Explanation:

This can be solved using the pattern for the square of a sum:

### Example Question #5 : How To Multiply Variables

Simplify:

Explanation:

This can be solved using the pattern for the square of a difference:

### Example Question #6 : How To Multiply Variables

Simplify:

Explanation:

This can be solved using the pattern for the square of a sum:

Multiply:

Explanation:

### Example Question #8 : How To Multiply Variables

Multiply:

Explanation:

Use the FOIL method:

### Example Question #9 : How To Multiply Variables

Define

What is  ?

Explanation:

Substitute  for :

Simplify: