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Age Problems

Age problems are a very popular type of algebra word problem. In age problems, you are given information so you can find the ages of the people in the problem.

For this topic, you will need to know how to create equations with variables and solve for variables.

Example 1:

Solve the following age problems.
Mike is 18 years old. The sum of the ages of Mike and Peter is 39.
How old is Peter?

 Mike = 18 Mike is 18 years old. Mike + Peter = 39 The sum of the ages of Mike and Peter is 39. 18 + Peter = 39 Substitute Peter = 39 - 18 Peter = 21

Peter is 21 years old. The answer is .

Example 2:

Solve the following age problems.
8 years from now Mary will be 19 years old. The current sum of the ages of Mary and Jose is 41.
How old is Jose right now?

 Mary + 8 = 19 After 8 years, Mary will be 19 years old. Mary = 19 - 8 Mary = 11 Right now, Mary is 11 years old. Mary + Jose = 41 The current sum of the ages of Mary and Jose is 41. 11 + Jose = 41 Substitute Jose = 41 - 11 Jose = 30

Jose is 30 years old right now. The answer is .

Example 3:

Solve the following age problems.
5 years from now Kate will be 48 years old. In 10 years, the sum of the ages of Kate and Sharon will be 90.
How old is Sharon right now?

 Kate + 5 = 48 After 5 years, Kate will be 48 years old. Kate = 48 - 5 Kate = 43 Right now, Kate is 43 years old. (Kate + 10) + (Sharon + 10) = 90 In 10 years, the sum of the ages of Kate and Sharon will be 90. (43 + 10) + (Sharon + 10) = 90 Substitute Sharon + 63 = 90 Sharon = 90 - 63 Sharon = 27

Sharon is 27 right now. The answer is .

Example 4:

Solve the following age problems.
13 years from now David will be twice as old as Pearl. The current sum of the ages of David and Pearl is 19.
How old is Pearl right now?

 David + Pearl = 19 The current sum of the ages of David and Pearl is 19. David = 19 - Pearl David's age in terms of Pearl's age. David + 13 = 2 × (Pearl + 13) 13 years from now, David will be twice as old as Pearl. (19 - Pearl) + 13 = 2 × (Pearl + 13) Substitute 32 - Pearl = 2(Pearl) + 26 32 = 3(Pearl) + 26 6 = 3(Pearl) 2 = Pearl

Pearl is 2 years old right now. The answer is .

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