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A parent is 3 times as old as their child. Together they are 56. How old is each?

The child is 14 and the parent is 42.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 3 times as old, so the parent is 3x.

  2. 2

    Together they are 56:

    x+3x=56x + 3x = 56
  3. 3

    Combine the x terms and divide:

    4x=56 ⇒ x=564=144x = 56\ \Rightarrow\ x = \frac{56}{4} = 14
  4. 4

    The parent is 3 × 14 = 42.

  5. 5

    Check: 14 + 42 = 56 ✓ and 42 = 3 × 14 ✓.

LaTeX source of the formulas on this page
\[ x + 3x = 56\ \Rightarrow\ x = 14 \]
\[ x + 3x = 56 \]
\[ 4x = 56\ \Rightarrow\ x = \frac{56}{4} = 14 \]

Questions

How old is the child?

14.

How old is the parent?

42.

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    Parent is 3 times the child's age, total 56: 42 and 14 | WordGPT