1. Polynomial Word Problems – Age
Algebra 1 Section 9.4c

2. 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.

3. Video Clip

4. 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

5. 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

6. 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
Richard x
x + 6
(x ) + (x + 6) = 35
2x + 17 = 35
Richard is 9 years old Jose is 14 years old
2x = 18
x = 9

7. 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

8. (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 = x
45 = 30 + x
15 years
15 = x

9. (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

10. 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

11. 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

12. Homework