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A parent is 4 times as old as their child. Together they are 85. How old is each?

The child is 17 and the parent is 68.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 4 times as old, so the parent is 4x.

  2. 2

    Together they are 85:

    x+4x=85x + 4x = 85
  3. 3

    Combine the x terms and divide:

    5x=85 ⇒ x=855=175x = 85\ \Rightarrow\ x = \frac{85}{5} = 17
  4. 4

    The parent is 4 × 17 = 68.

  5. 5

    Check: 17 + 68 = 85 ✓ and 68 = 4 × 17 ✓.

LaTeX source of the formulas on this page
\[ x + 4x = 85\ \Rightarrow\ x = 17 \]
\[ x + 4x = 85 \]
\[ 5x = 85\ \Rightarrow\ x = \frac{85}{5} = 17 \]

Questions

How old is the child?

17.

How old is the parent?

68.

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    Parent is 4 times the child's age, total 85: 68 and 17 | WordGPT