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A parent is 4 times as old as their child. Together they are 50. How old is each?

The child is 10 and the parent is 40.

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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 50:

    x+4x=50x + 4x = 50
  3. 3

    Combine the x terms and divide:

    5x=50 ⇒ x=505=105x = 50\ \Rightarrow\ x = \frac{50}{5} = 10
  4. 4

    The parent is 4 × 10 = 40.

  5. 5

    Check: 10 + 40 = 50 ✓ and 40 = 4 × 10 ✓.

LaTeX source of the formulas on this page
\[ x + 4x = 50\ \Rightarrow\ x = 10 \]
\[ x + 4x = 50 \]
\[ 5x = 50\ \Rightarrow\ x = \frac{50}{5} = 10 \]

Questions

How old is the child?

10.

How old is the parent?

40.

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    Parent is 4 times the child's age, total 50: 40 and 10 | WordGPT