Alex is six years older than his sister, Emma. The sum of their ages is 32. How old is Alex?

First, assume Alex is X years old and that Emma is Y years old.

Since Alex is 6 years older than Emma, it means X - 6 = Y.

Since the sum of their ages is 32, it means X + Y = 32.

Substitute the Y in the second equation with X - 6 to get X + (X-6) = 32. This is simplified to 2X - 6 = 32 or 2X = 38. Solving the equation for X gets that X = 19.

This means Alex is 19.

Let Emma = e, Alex = 6+e because he is 6 years older than Emma. Since their sum is 32, you would add e + (6+e) = 32 and solve for e.

e + (6+e) = 32

6+2e=32

2e=32-6

2e=26

e=26/2

e=13

So Emma is 13, Alex is 13+6=19 years old.