Translating Word Problems into Equations
Cameron is three years younger than Ezra. If the combined age of Cameron and Ezra is seventeen years, how old was Ezra one year ago?
Read the question carefully. This problem is very easy to solve, but you might fall into a trap if you do not pay close attention to the question. Be sure to note that they are asking for Ezra’s age one year ago.
Identify the bottom line. Find Ezra’s age one year ago.
Assess your options. You can try to solve this problem in your head, but you might not be able to keep the names and ages straight without writing them down. It is just as easy (and almost as quick) to convert the language of the problem into a math equation that you can solve. Make note of how the following mathematical operations translate into words. This information may help you on future problems as well!
“is, was, has, costs”
“combine, sum of, greater than, more than, older than, farther than”
“difference, less than, fewer, younger than”
Attack the problem. Use the translations above to convert the problem into equations and solve.
1. Cameron is three years younger than Ezra. Translation: C = E – 3
2. The combined age of Cameron and Ezra is seventeen years. Translation: C + E = 17
3. Solve the equations.
C = E – 3
C + E = 17
E – 3 + E = 17
2E – 3 = 17
2E = 20
E = 10
Loop back. Did you find what you were looking for? The problem asked for Ezra’s age one year ago. One year ago, Ezra was 9, so the answer is C. Answer choice D is obviously a trap.
The correct answer is (C).
This is a medium level problem.