Question

A mother is 26 years older than her daughter. The daughter is one-third her mother's age. How old is each now? When will the mother be twice as old as her daughter?
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Answer 1

Answer:

• now: daughter: 13, mother: 39
• then: daughter: 26, mother: 52

Step-by-step explanation:

If the daughter's age is 1/3 the mother's age, the difference in their ages is ...

  1-1/3 = 2/3

the mother's age. The daughter's age is half that (1/3 the mother's age), so the daughter's age is 26/2 = 13 years. The mother's age is 13+26 = 39 years, which is 3 times the daughter's age.

The daughter is 13 now; the mother is 39.

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When the mother is twice as old, the daughter's age will be equal to their age difference: 26. The mother's age will be 26 +26 = 52

When the mother is twice as old, she will be 52, and the daughter will be 26.

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Additional comment

You can assign variables and write equations that will give you the same result. If you let d and m represent the daughter's age and the mother's age, respectively, you could write the system ...

  m = d +26

  d = m/3

Substituting for d, you get ...

  m = m/3 +26

  2/3m = 26 . . . . . . subtract m/3

Note that this is the relationship we came to in the discussion above.

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When an age difference is given, you know it will remain the same throughout the problem. Everybody ages at the same rate, so the difference is constant. As we have done above, it is often useful to compare the age difference to the difference in ratio units. This tells you the size of a ratio unit.