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A parent is 6 times as old as their child. Together they are 84. How old is each?

The child is 12 and the parent is 72.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 6 times as old, so the parent is 6x.

  2. 2

    Together they are 84:

    x+6x=84x + 6x = 84
  3. 3

    Combine the x terms and divide:

    7x=84 ⇒ x=847=127x = 84\ \Rightarrow\ x = \frac{84}{7} = 12
  4. 4

    The parent is 6 × 12 = 72.

  5. 5

    Check: 12 + 72 = 84 ✓ and 72 = 6 × 12 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 84\ \Rightarrow\ x = 12 \]
\[ x + 6x = 84 \]
\[ 7x = 84\ \Rightarrow\ x = \frac{84}{7} = 12 \]

Questions

How old is the child?

12.

How old is the parent?

72.

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    Parent is 6 times the child's age, total 84: 72 and 12 | WordGPT