### How to Set Up Basic Equations

You will see problems on the test that ask you to make basic equations from the information provided.

You will need to read the problem carefully and then express the facts in terms of an algebraic equation.

These types of questions are often practical problems that involve buying or selling merchandise.

**Example 1:**

A company purchases cell phones at a cost of *x* and sells the cell phones at four times the cost.

What equation below represents the profit made on each cell phone?

A. *x*

B. 3*x*

C. 4*x*

D. 3 − *x*

E. 4 − *x*

**The correct answer is B.**

The sales price of each cell phone is four times the cost.

The cost is expressed as *x*, so the sales price is 4*x*.

The difference between the sales price of each cell phone and the cost of each cell phone is the profit.

REMEMBER: Sales Price − Cost = Profit

In this problem, the sales price is 4*x* and the cost is *x*.

4*x* − *x* = Profit

3*x* = Profit

**Example 2:**

An internet provider sells internet packages based on low monthly rates. The price for the internet service depends on the speed of the internet connection. The chart below indicates the prices of the various internet packages:

Price in dollars (P) |
10 | 20 | 30 | 40 |

Gigabyte speed (s) |
2 | 4 | 6 | 8 |

Which equation represents the prices of these internet packages?

F. *P* = (*s* – 5) × 5

G. *P* = (*s* + 5) × 5

H. *P* = 5 ÷ *s*

I. *P* = *s* × 5

J. *P* = *s* ÷ 5

**The correct answer is I.**

The price of the internet connection is always 5 times more than the speed.

10 ÷ 2 = 5

20 ÷ 4 = 5

30 ÷ 6 = 5

40 ÷ 8 = 5

So the price of the internet connection (represented by variable *P*) equals the speed (represented by variable *s*) times 5:

*P* = *s* × 5

Go Back to the **Elementary Algebra Page**

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