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A parent is 3 times as old as their child. Together they are 72. How old is each?

The child is 18 and the parent is 54.

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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 72:

    x+3x=72x + 3x = 72
  3. 3

    Combine the x terms and divide:

    4x=72 ⇒ x=724=184x = 72\ \Rightarrow\ x = \frac{72}{4} = 18
  4. 4

    The parent is 3 × 18 = 54.

  5. 5

    Check: 18 + 54 = 72 ✓ and 54 = 3 × 18 ✓.

LaTeX source of the formulas on this page
\[ x + 3x = 72\ \Rightarrow\ x = 18 \]
\[ x + 3x = 72 \]
\[ 4x = 72\ \Rightarrow\ x = \frac{72}{4} = 18 \]

Questions

How old is the child?

18.

How old is the parent?

54.

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    Parent is 3 times the child's age, total 72: 54 and 18 | WordGPT