Solving Story Problems with Algebra

1. Solving Story Problems with Algebra

2. The sum of the ages of Joe, Mandy, and Rinaldo is 70. Joe is 4 years older than Mandy and Rinaldo is 6 years younger than Mandy. How old is Joe? • Let’s letn stand for Mandy’s age because the clues all relate to her age. If n is Mandy’s age, then whose age would be n + 4 ? Joe Whose age would be n – 6 ? Rinaldo So Mandy’s age is n, Joe’s age is (n + 4) and Rinaldo’s age is (n – 6). If you add Mandy’s age and Joe’s age and Rinaldo’s age, you get 70. How could you set up an equation to solve for Mandy’s age? n + (n + 4) + (n – 6) = 70

3. n + n + 4 + n – 6 = 70 Combine like terms. 4 – 6 = -2 n + n + n = 3n So, 3n – 2 = 70 + 2 + 2 Add 2 to the left to get rid of – 2. Add 2 to the right side to keep it balanced.

4. Now you have 3n = 72 ÷ 3 ÷ 3 Divide by 3 on the left to get rid of multiplying by 3. Divide by 3 on the right side to keep it balanced.

5. Now you have n by itself, equal to 72 ÷ 3. n = 24 We now know that Mandy is 24. How old is Joe? n + 4 = 28 Joe is 28.

6. Check to see if the age for Joe works for the equation. Mandy’s age plus Joe’s age plus Rinaldo’s age equals 70. Mandy’s age: 24 Plus Joe’s age: 28 Plus Rinaldo’s age: + 18 70