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A parent is 5 times as old as their child. Together they are 90. How old is each?

The child is 15 and the parent is 75.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 5 times as old, so the parent is 5x.

  2. 2

    Together they are 90:

    x+5x=90x + 5x = 90
  3. 3

    Combine the x terms and divide:

    6x=90 ⇒ x=906=156x = 90\ \Rightarrow\ x = \frac{90}{6} = 15
  4. 4

    The parent is 5 × 15 = 75.

  5. 5

    Check: 15 + 75 = 90 ✓ and 75 = 5 × 15 ✓.

LaTeX source of the formulas on this page
\[ x + 5x = 90\ \Rightarrow\ x = 15 \]
\[ x + 5x = 90 \]
\[ 6x = 90\ \Rightarrow\ x = \frac{90}{6} = 15 \]

Questions

How old is the child?

15.

How old is the parent?

75.

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    Parent is 5 times the child's age, total 90: 75 and 15 | WordGPT