Page 61 - MarceAlgebra Demystified

48 CHAPTER 2 Introduction to Variables

7x 2 7x 5 2 8 35x 16 35x þ 16
9: þ ¼ þ ¼ þ ¼
24y 15y 24y 5 15y 8 120y 120y 120y

3 2 3 5x 2 2y 15x 4y 15x þ 4y
10: þ ¼ þ ¼ þ ¼
14y 35x 14y 5x 35x 2y 70xy 70xy 70xy

Word Problems

Often the equations used to solve word problems should have only one
variable, and other unknowns must be written in terms of one variable.
The goal of this section is to get you acquainted with setting your variable
equal to an appropriate unknown quantity, and writing other unknown
quantities in terms of the variable.

Examples

Andrea is twice as old as Sarah.

Because Andrea’s age is being compared to Sarah’s, the easiest thing to
do is to let x represent Sarah’s age:

Let x ¼ Sarah’s age.

Andrea is twice as old as Sarah, so Andrea’s age ¼ 2x. We could have
let x represent Andrea’s age, but we would have to re-think the state-
ment as ‘‘Sarah is half as old as Andrea.’’ This would mean Sarah’s age
1
would be represented by x.
2
John has eight more nickels than Larry has.

The number of John’s nickels is being compared to the number of
Larry’s nickels, so it is easier to let x represent the number of nickels
Larry has.

Let x ¼ the number of nickels Larry has.

x þ 8 ¼ the number of nickels John has.

A used car costs $5000 less than a new car.