Question 73899
LET A = Mary's present age and B = Mark's present age.
10 years ago, Mary's age was A-10 and Mark's age was B-10.
From the problem description, we can write:
1) A-10 = 5(B-10) or A = 5B-40
Twenty years hence, Mary's age will be A+20 and Mark's age will be B+20.
From the problem description, we can write:
2) A+20 = 2(B+20) or A = 2B+20
Set equation 1) equal to equation 2) and solve for B (Mark's present age)
5B-40 = 2B+20 Subtract 2B from both sides.
3B-40 = 20 Add 40 to both sides.
3B = 60 Divide both sides by 3.
B = 20  This is Mark's present age.
From equation 1) we get:
A = 2B+20
A = 2(20)+20
A = 40+20
A = 60 This is Mary's present age.
Check:
A-10 = 5(B-10)
60-10 = 5(20-10)
50 = 5(10)
50 = 50
and...
A+20 = 2(B+20)
60+20 = 2(20+20)
80 = 2(40)
80 = 80