So far in this unit we've been looking at algebraic expressions. But if all you've got is an algebraic expression, you don't have a word problem; to be a word problem, an equation is required. An equation is two algebraic expressions combined with an equals sign.

How do you know where to put an equals sign? Well, there are a few keywords that often are used to represent "equals". Some of these are listed below:

is, are, were (and other forms of the verb "to be!"), adds up to, gives, yields, equals, results in

Sample #1

n and 5 add up to 13.

Equation #1

The phrase "add up to" breaks the problem into two parts. The left side (before the phrase "add up to") is "n + 5," and the right side is just "13." So the equation is the left and right sides, with an equals sign between them:

n + 5 = 13

Sample #2

The product of two and a number is four more than the number.

Equation #2

The two expressions are "2n" and "4 + n", so the equation is:

2n = 4 + n

Sample #3

The product of four more than a number and four less than a number yields two less than five times the number.

Equation #3

Here the "equals" word is "yields." The equation is:

(n + 4)(n - 4) = 5n - 2

For each problem below, you don't need to solve the word problem; just write the equation you would use to solve it.

1.

If five is decreased by the sum of n and 2, the result is 1.

2.

The sum of a number and twice that number is 14 more than the number.

3.

Joe's age is twice what it was ten years ago.

4.

If the price of a book is increased by four dollars, the result is $15.95

5.

The price of an item is marked down 10%, and the resulting cost is $18

6.

The ratio of x to 7 is four less than x.

7.

The product of four less than a number and three more than a number is equal to two less than eight times the number.

8.

Four less than four times a number is equal to the square of that number.

9.

If the temperature starts at 32 degrees, and increases at a rate of 4 degrees per hour for a certain number of hours, the resulting temperature is 92 degrees.

10.

If the population of Oxford increases by 450 every year for 10 years, the resulting population is twice the original population.