The sum of jason and mandy age is 35. ten years ago jason was double mandy age. how old are they now?

Jason is 20 and Mandy is 15.

Let j be Jason's age and m be Mandy's age.

Then j+m=35.  Solving this for j, we have
j = 35 - m

Jason's age 10 years ago can be represented by j-10 and Mandy's age 10 years ago can be represented by m-10:
(j-10)=2(m-10)

Using the distributive property, we have
j-10=2*m-2*10
j-10=2m-20

Substituting our value for j from the first equation in, we have
35-m-10 = 2m-20
25-m = 2m-20

Add m to both sides:
25-m+m = 2m-20+m
25=3m-20

Add 20 to both sides:
25+20=3m-20+20
45=3m

Divide both sides by 3:
45/3 = 3m/3
15=m

Mandy is 15.
Jason is 35-15=20.