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A parent is 4 times as old as their child. Together they are 65. How old is each?

The child is 13 and the parent is 52.

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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 65:

    x+4x=65x + 4x = 65
  3. 3

    Combine the x terms and divide:

    5x=65 ⇒ x=655=135x = 65\ \Rightarrow\ x = \frac{65}{5} = 13
  4. 4

    The parent is 4 × 13 = 52.

  5. 5

    Check: 13 + 52 = 65 ✓ and 52 = 4 × 13 ✓.

LaTeX source of the formulas on this page
\[ x + 4x = 65\ \Rightarrow\ x = 13 \]
\[ x + 4x = 65 \]
\[ 5x = 65\ \Rightarrow\ x = \frac{65}{5} = 13 \]

Questions

How old is the child?

13.

How old is the parent?

52.

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    Parent is 4 times the child's age, total 65: 52 and 13 | WordGPT