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A parent is 6 times as old as their child. Together they are 70. How old is each?

The child is 10 and the parent is 60.

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How to work it out

  1. 1

    Let x be the child's age. The parent is 6 times as old, so the parent is 6x.

  2. 2

    Together they are 70:

    x+6x=70x + 6x = 70
  3. 3

    Combine the x terms and divide:

    7x=70 ⇒ x=707=107x = 70\ \Rightarrow\ x = \frac{70}{7} = 10
  4. 4

    The parent is 6 × 10 = 60.

  5. 5

    Check: 10 + 60 = 70 ✓ and 60 = 6 × 10 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 70\ \Rightarrow\ x = 10 \]
\[ x + 6x = 70 \]
\[ 7x = 70\ \Rightarrow\ x = \frac{70}{7} = 10 \]

Questions

How old is the child?

10.

How old is the parent?

60.

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    Parent is 6 times the child's age, total 70: 60 and 10 | WordGPT