If Mary is now ?18?, how old will John be seven years from now? Suppose we’d been given the following word problem instead:Ĭurrently, John’s age is four less than twice Mary’s age. Since we defined ?y? as John’s age, the answer is ?32?. The final step is to answer the question that was asked. Here, we’re given Mary’s age as ?18?, so we substitute ?18? for ?x? and then solve for ?y?. The third step in solving a word problem is to use the given data and solve the equation. To see this, it may help to think of the word “is” as having the same meaning (in math) as “is equal to.”Ĭombining all of these, we get the equation How about the word “is” (in “John’s age is four less than twice Mary’s age”)? Well, “is” is translated as an equals sign. Here, “John’s age” is translated as “?2x-4?.” The next step in solving a word problem is to “translate” each word or phrase into mathematical symbols. So we’ll define the variables by saying “Let ?x? be Mary’s age, and let ?y? be John’s age.” (We could use any letters of the alphabet for the variables, but people often use ?x? for one of the variables, and if there are one or two additional variables, they tend to use ?y? and ?z?, in that order.) In this problem, we have two quantities: Mary’s age and John’s age. What that means is to state the particular quantity that each variable stands for. The first step in solving a word problem like this is to define the variables. John’s age is four less than twice Mary’s age. Not only can we translate phrases into expressions, but we can write equations from some phrases as well.įor instance, suppose you wanted to use algebra to solve the following word problem:
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