A parent is 4 times as old as their child. Together they are 100. How old is each?

The child is 20 and the parent is 80.

x + 4x = 100\ \Rightarrow\ x = 20

How to work it out

1
Let x be the child's age. The parent is 4 times as old, so the parent is 4x.
2
Together they are 100:
$x + 4x = 100$
3
Combine the x terms and divide:
$5x = 100\ \Rightarrow\ x = \frac{100}{5} = 20$
4
The parent is 4 × 20 = 80.
5
Check: 20 + 80 = 100 ✓ and 80 = 4 × 20 ✓.

LaTeX source of the formulas on this page

\[ x + 4x = 100\ \Rightarrow\ x = 20 \]
\[ x + 4x = 100 \]
\[ 5x = 100\ \Rightarrow\ x = \frac{100}{5} = 20 \]

How old is the child?

20.

How old is the parent?

80.