Often the most challenging aspect of algebra problems is the odd way in which information is presented. Don’t get frustrated; just break down the information into small pieces and take things one step at a time. Word problems can usually be translated from left to right, but this is not always the case. Say you see this sentence: “The number of stamps in George’s stamp collection is twice the number that is 5 less than the number of stamps in Bill’s stamp collection.” Instead of trying to translate it into math all in one step, approach it piece by piece.
Whenever possible, choose letters for the variables that make sense in the context of the problem. For example, start by calling the number of stamps in George’s stamp collection G and the number of stamps in Bill’s stamp collection B. Now, think about the relationship between the two amounts: G is not compared to B but to 5 less than B, or (B − 5). So G is twice as large as (B − 5). To set them equal to each other, multiply (B − 5) by two. The equation is G = 2(B − 5).
The hardest part of word problems is the process of taking the English sentences and extracting the math from them. The actual math in word problems tends to be the easiest part. The following translation table will help you start dealing with English-to-math translation:
| Word Problems Translation Table | |
| English | Math |
| equals, is, was, will be, has, costs, adds up to, the same as, as much as | = |
| times, of, multiplied by, product of, twice, double, by | × |
| divided by, per, out of, each, ratio | ÷ |
| plus, added to, and, sum, combined | + |
| minus, subtracted from, smaller than, less than, fewer, decreased by, difference between | − |
| a number, how much, how many, what | x, n, etc. |
Example:
w is x less than y.
Solution:
w = y − x
Example:
Giuseppa’s weight is 75 pounds more than twice Jovanna’s weight.
Solution:
G = 2J + 75
Example:
In 5 years, Sandy will be 4 years younger than twice Tina’s age.
Solution:
(S + 5) = 2(T + 5) − 4
Notice here that the statement discusses the ages of Sandy and Tina in five years, so you must represent their ages as (S + 5) and (T + 5), respectively. One common mistake is to translate the right side of the equation as 2T + 5 − 4, but that is not equivalent to 2(T + 5) − 4.
Example:
The sum of Richard’s age and Cindy’s age in years is 17 more than the amount by which Tim’s age is greater than Kathy’s age.
Solution:
R + C = (T − K) + 17