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A parent is 6 times as old as their child. Together they are 56. How old is each?

The child is 8 and the parent is 48.

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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 56:

    x+6x=56x + 6x = 56
  3. 3

    Combine the x terms and divide:

    7x=56 ⇒ x=567=87x = 56\ \Rightarrow\ x = \frac{56}{7} = 8
  4. 4

    The parent is 6 × 8 = 48.

  5. 5

    Check: 8 + 48 = 56 ✓ and 48 = 6 × 8 ✓.

LaTeX source of the formulas on this page
\[ x + 6x = 56\ \Rightarrow\ x = 8 \]
\[ x + 6x = 56 \]
\[ 7x = 56\ \Rightarrow\ x = \frac{56}{7} = 8 \]

Questions

How old is the child?

8.

How old is the parent?

48.

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    Parent is 6 times the child's age, total 56: 48 and 8 | WordGPT