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A parent is 6 times as old as their child. Together they are 77. How old is each?

The child is 11 and the parent is 66.

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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 77:

    x+6x=77x + 6x = 77
  3. 3

    Combine the x terms and divide:

    7x=77 ⇒ x=777=117x = 77\ \Rightarrow\ x = \frac{77}{7} = 11
  4. 4

    The parent is 6 × 11 = 66.

  5. 5

    Check: 11 + 66 = 77 ✓ and 66 = 6 × 11 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 77\ \Rightarrow\ x = 11 \]
\[ x + 6x = 77 \]
\[ 7x = 77\ \Rightarrow\ x = \frac{77}{7} = 11 \]

Questions

How old is the child?

11.

How old is the parent?

66.

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    Parent is 6 times the child's age, total 77: 66 and 11 | WordGPT