# How to Work with Coefficients

Algebra simplifies expressions with coefficients*,* which are numbers preceding variables. For example, 3 is the coefficient in 3*x*. Rather than using a multiplication sign between 3 and *x, *the number is just written in front of a variable*,* which means that the 3 and *x* are multiplied together. Instead of writing *a** *+ *a** *+ *a** *+ *a**, *you can express it as 4*a**, *with 4 being the coefficient.

When several variables are multiplied together, multiplication symbols aren’t needed. The term 3*xyz* means that all four factors are multiplied together.

You can use variables to simplify the following exercise: Collect, organize, and report on the coins collected during a charity drive.

Set up your variables.

Let

*n*represent the value of the nickels in a roll of nickels.Let

*d*represent the value of the dimes in a roll of dimes.Let

*q*represent the value of the quarters in a roll of quarters.After collecting the money, you get the following information from your helpers:

Ann collected six rolls of nickels, four rolls of dimes, and nine rolls of quarters, or 6

*n*+ 4*d*+ 9*q.*Ben collected five rolls of nickels, three rolls of dimes, and seven rolls of quarters, or 5

*n*+ 3*d*+ 7*q.*Cal collected 15 rolls of nickels, two rolls of dimes, and six rolls of quarters, or 15

*n*+ 2*d*+ 6*q.*Don collected one roll of nickels, three rolls of dimes, and four rolls of quarters, or

*n*+ 3*d*+ 4*q.*Set up an equation to add all the rolls of nickels, dimes, and quarters:

Compute the total amount of money raised.

A roll of nickels is worth $2, so

*n*A roll of dimes is worth $5, so

*d*A roll of quarters is worth $10, so

*q*= 10.A total of $374 was raised.