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A parent is 6 times as old as their child. Together they are 42. How old is each?

The child is 6 and the parent is 36.

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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 42:

    x+6x=42x + 6x = 42
  3. 3

    Combine the x terms and divide:

    7x=42 ⇒ x=427=67x = 42\ \Rightarrow\ x = \frac{42}{7} = 6
  4. 4

    The parent is 6 × 6 = 36.

  5. 5

    Check: 6 + 36 = 42 ✓ and 36 = 6 × 6 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 42\ \Rightarrow\ x = 6 \]
\[ x + 6x = 42 \]
\[ 7x = 42\ \Rightarrow\ x = \frac{42}{7} = 6 \]

Questions

How old is the child?

6.

How old is the parent?

36.

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    Parent is 6 times the child's age, total 42: 36 and 6 | WordGPT