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A parent is 5 times as old as their child. Together they are 54. How old is each?

The child is 9 and the parent is 45.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 5 times as old, so the parent is 5x.

  2. 2

    Together they are 54:

    x+5x=54x + 5x = 54
  3. 3

    Combine the x terms and divide:

    6x=54 ⇒ x=546=96x = 54\ \Rightarrow\ x = \frac{54}{6} = 9
  4. 4

    The parent is 5 × 9 = 45.

  5. 5

    Check: 9 + 45 = 54 ✓ and 45 = 5 × 9 ✓.

LaTeX source of the formulas on this page
\[ x + 5x = 54\ \Rightarrow\ x = 9 \]
\[ x + 5x = 54 \]
\[ 6x = 54\ \Rightarrow\ x = \frac{54}{6} = 9 \]

Questions

How old is the child?

9.

How old is the parent?

45.

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    Parent is 5 times the child's age, total 54: 45 and 9 | WordGPT