Polynomial Word Problems – Age

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Polynomial Word Problems – Age Algebra 1 Section 9.4c

Steps 1. Read the entire problem. 2. Read the problem again and identify the important facts. 3. Set up a comparison and/or table. 4. Read the problem again and set up an equation. 5. Solve the equation. 6. Read the problem one last time to determine what answer is needed.

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x + (x + 13) = 55 2x + 13 = 55 2x = 42 x = 21 Maria is 34 years old Age Problems Example 1 Marie is 13 years older than Joanna. The sum of their ages is 55. How old is Maria? Marie = x + 13 (34) Joanna = x (21) x + (x + 13) = 55 2x + 13 = 55 2x = 42 x = 21 Maria is 34 years old

Maria is 39 years old Her son is 13 years old Age Problems Example 2 Ms Jones is 3 times as old as her son. The sum of their ages is 52. What are their ages? Mom = 3x (39) Son = x (13) x + 3x = 52 4x = 52 x = 13 Maria is 39 years old Her son is 13 years old

Richard is 9 years old Jose is 14 years old 2x = 18 x = 9 Age Problems Example 3 Jose is 5 years older than Richard. In 6 years, the sum of their ages will be 35. How old is each person now? Age now In six years Jose x + 5 x + 5 + 6 Richard x x + 6 (x + 5 + 6) + (x + 6) = 35 2x + 17 = 35 Richard is 9 years old Jose is 14 years old 2x = 18 x = 9

Erik is 12 years old Dan is 24 years old 3x = 36 x = 12 Age Problems Example 4 Dan is twice as old as Erik. Five years ago, the sum of their ages was 26. How old are they now? Age now Five years ago Dan 2x 2x – 5 Erik x x – 5 (2x – 5) + (x – 5) = 26 3x – 10 = 26 Erik is 12 years old Dan is 24 years old 3x = 36 x = 12

(45 + x) = 2(15 + x) 45 + x = 30 + 2x 45 = 30 + x 15 years 15 = x Age Problems Example 5 If you are 15 years old and your father is 45 years old, in how many years will your father be twice as old as you? Age Now Age Later You 15 15 + x Father 45 45 + x (45 + x) = 2(15 + x) 45 + x = 30 + 2x 45 = 30 + x 15 years 15 = x

(50 – x) = 2(29 – x) 50 – x = 58 – 2x x = 8 8 years ago Age Problems Example 6 Rose is 29 years old. Her mother is 50. How many years ago was the mother twice as old as Rose? Age Now Previous Age Rose 29 29 – x Mom 50 50 – x (50 – x) = 2(29 – x) 50 – x = 58 – 2x x = 8 8 years ago

Younger sister is 15 years old. Older sister is 17 years old. Age Problems Example 7 The ages of two sisters are consecutive odd integers. Twelve years ago, the sum of the ages was 8. How old is each now? Younger sister is 15 years old. Older sister is 17 years old. Age Now Twelve years ago Younger x x – 12 Older x + 2 (x + 2) – 12 (x – 12) + [(x + 2) – 12] = 8 2x – 22 = 8 2x = 30 x = 15

17 + x = ½(50 + x) 34 + 2x = 50 + x x = 16 16 years Age Problems Example 8 Emil, who just turned 17, has a 50-year-old aunt. In how many years will Emil be half as old as his aunt? Age Now Future Age Emil 17 17 + x Aunt 50 50 + x 17 + x = ½(50 + x) 34 + 2x = 50 + x x = 16 16 years

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