Variables in Word Problems Help

Example 1:

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 = Sarah’s age.

Andrea is twice as old as Sarah, so Andrea’s age = 2 x . We could have let x represent Andrea’s age, but we would have to re-think the statement as “Sarah is half as old as Andrea.” This would mean Sarah’s age would be represented by .

Example 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 = the number of nickels Larry has.

x + 8 = the number of nickels John has.

Example 3:

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

Let x = the price of the new car.

x – 5000 = the price of the used car

Example 4:

A box’s length is three times its width.

Let x = width (in the given units).

3 x = length (in the given units)

Example 5:

Jack is two-thirds as tall as Jill.

Let x = Jill’s height (in the given units).

= Jack’s height (in the given units)

Example 6:

From 6 pm to 6 am the temperature dropped 30 degrees.

Let x = temperature (in degrees) at 6 pm.

x – 30 = temperature (in degrees) at 6 am

Example 7:

One-eighth of an employee’s time is spent cleaning his work station.

Let x = the number of hours he is on the job.

= the number of hours he spends cleaning his work station

Example 8:

$10,000 was deposited between two savings accounts, Account A and Account B.

Let x = amount deposited in Account A.

How much is left to represent the amount invested in Account B? If x dollars is taken from $10,000, then it must be that 10,000 – x dollars is left to be deposited in Account B.

Or if x represents the amount deposited in Account B, then 10,000 – x dollars is left to be deposited in Account A.

Example 9:

A wire is cut into three pieces of unequal length. The shortest piece is the length of the longest piece, and the middle piece is the length of the longest piece.

Let x = length of the longest piece.

Example 10:

A store is having a one-third off sale on a certain model of air conditioner.

Let x = regular price of the air conditioner. Then = sale price of the air conditioner.

We cannot say that the sale price is because is not “one-third off the price of the air conditioner;” it is simply “one-third.” “One-third the price of the air conditioner” is represented by . “One-third off the price of the air conditioner” is represented by