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A parent is 5 times as old as their child. Together they are 78. How old is each?

The child is 13 and the parent is 65.

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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 78:

    x+5x=78x + 5x = 78
  3. 3

    Combine the x terms and divide:

    6x=78 ⇒ x=786=136x = 78\ \Rightarrow\ x = \frac{78}{6} = 13
  4. 4

    The parent is 5 × 13 = 65.

  5. 5

    Check: 13 + 65 = 78 ✓ and 65 = 5 × 13 ✓.

LaTeX source of the formulas on this page
\[ x + 5x = 78\ \Rightarrow\ x = 13 \]
\[ x + 5x = 78 \]
\[ 6x = 78\ \Rightarrow\ x = \frac{78}{6} = 13 \]

Questions

How old is the child?

13.

How old is the parent?

65.

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    Parent is 5 times the child's age, total 78: 65 and 13 | WordGPT