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Example 5.37 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.37
Translate to a system of equations and then solve:
Devon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for the ages of Devon and Cooper. Step 3. Name what we are looking for. Let Devon’s age.
Cooper’s ageStep 4. Translate into a system of equations. Devon is 26 years older than Cooper. The sum of their ages is 50. The system is: Step 5. Solve the system of equations.
Solve by substitution.Substitute c + 26 into the second equation. Solve for c. Substitute c = 12 into the first equation and then solve for d. Step 6. Check the answer in the problem. Is Devon’s age 26 more than Cooper’s?
Yes, 38 is 26 more than 12.
Is the sum of their ages 50?
Yes, 38 plus 12 is 50.Step 7. Answer the question. Devon is 38 and Cooper is 12 years old.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and then solve:
Ali is 12 years older than his youngest sister, Jameela. The sum of their ages is 40. Find their ages.
How did it go?