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A parent is 6 times as old as their child. Together they are 21. How old is each?

The child is 3 and the parent is 18.

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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 21:

    x+6x=21x + 6x = 21
  3. 3

    Combine the x terms and divide:

    7x=21 ⇒ x=217=37x = 21\ \Rightarrow\ x = \frac{21}{7} = 3
  4. 4

    The parent is 6 × 3 = 18.

  5. 5

    Check: 3 + 18 = 21 ✓ and 18 = 6 × 3 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 21\ \Rightarrow\ x = 3 \]
\[ x + 6x = 21 \]
\[ 7x = 21\ \Rightarrow\ x = \frac{21}{7} = 3 \]

Questions

How old is the child?

3.

How old is the parent?

18.

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    Parent is 6 times the child's age, total 21: 18 and 3 | WordGPT