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A parent is 4 times as old as their child. Together they are 30. How old is each?

The child is 6 and the parent is 24.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 4 times as old, so the parent is 4x.

  2. 2

    Together they are 30:

    x+4x=30x + 4x = 30
  3. 3

    Combine the x terms and divide:

    5x=30 ⇒ x=305=65x = 30\ \Rightarrow\ x = \frac{30}{5} = 6
  4. 4

    The parent is 4 × 6 = 24.

  5. 5

    Check: 6 + 24 = 30 ✓ and 24 = 4 × 6 ✓.

LaTeX source of the formulas on this page
\[ x + 4x = 30\ \Rightarrow\ x = 6 \]
\[ x + 4x = 30 \]
\[ 5x = 30\ \Rightarrow\ x = \frac{30}{5} = 6 \]

Questions

How old is the child?

6.

How old is the parent?

24.

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    Parent is 4 times the child's age, total 30: 24 and 6 | WordGPT