let

p = the age of Patrick now

a = the age of Amy now

Patrick is 4 years older than Amy:

p = 4 + a

In 10 years the sum of their ages will be 36:

10 + p + 10 + a = 36

p + a + 20 = 36

p + a = 36 - 20

p + a = 16

by solving the system of equations:

p = 4 + a

p + a = 16

we find:

p = 10 years

a = 6 years

click here to see the step by step solution of the system of equations:

Patrick is 10 years old now.

Amy is 4 years old now.