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A parent is 4 times as old as their child. Together they are 80. How old is each?

The child is 16 and the parent is 64.

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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 80:

    x+4x=80x + 4x = 80
  3. 3

    Combine the x terms and divide:

    5x=80 ⇒ x=805=165x = 80\ \Rightarrow\ x = \frac{80}{5} = 16
  4. 4

    The parent is 4 × 16 = 64.

  5. 5

    Check: 16 + 64 = 80 ✓ and 64 = 4 × 16 ✓.

LaTeX source of the formulas on this page
\[ x + 4x = 80\ \Rightarrow\ x = 16 \]
\[ x + 4x = 80 \]
\[ 5x = 80\ \Rightarrow\ x = \frac{80}{5} = 16 \]

Questions

How old is the child?

16.

How old is the parent?

64.

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    Parent is 4 times the child's age, total 80: 64 and 16 | WordGPT