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A parent is 3 times as old as their child. Together they are 52. How old is each?

The child is 13 and the parent is 39.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 3 times as old, so the parent is 3x.

  2. 2

    Together they are 52:

    x+3x=52x + 3x = 52
  3. 3

    Combine the x terms and divide:

    4x=52 ⇒ x=524=134x = 52\ \Rightarrow\ x = \frac{52}{4} = 13
  4. 4

    The parent is 3 × 13 = 39.

  5. 5

    Check: 13 + 39 = 52 ✓ and 39 = 3 × 13 ✓.

LaTeX source of the formulas on this page
\[ x + 3x = 52\ \Rightarrow\ x = 13 \]
\[ x + 3x = 52 \]
\[ 4x = 52\ \Rightarrow\ x = \frac{52}{4} = 13 \]

Questions

How old is the child?

13.

How old is the parent?

39.

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    Parent is 3 times the child's age, total 52: 39 and 13 | WordGPT