A parent is 3 times as old as their child. Together they are 100. How old is each?

The child is 25 and the parent is 75.

x + 3x = 100\ \Rightarrow\ x = 25

How to work it out

1
Let x be the child's age. The parent is 3 times as old, so the parent is 3x.
2
Together they are 100:
$x + 3x = 100$
3
Combine the x terms and divide:
$4x = 100\ \Rightarrow\ x = \frac{100}{4} = 25$
4
The parent is 3 × 25 = 75.
5
Check: 25 + 75 = 100 ✓ and 75 = 3 × 25 ✓.

LaTeX source of the formulas on this page

\[ x + 3x = 100\ \Rightarrow\ x = 25 \]
\[ x + 3x = 100 \]
\[ 4x = 100\ \Rightarrow\ x = \frac{100}{4} = 25 \]

How old is the child?

25.

How old is the parent?

75.