Answer:
4years
Step-by-step explanation:
Let the present age of Mark be x
Let the present age of Max be y
Five years ago
Mark = x-5
Max = y - 5
If mark was twice as old as Max, then;
x - 5 = 2(y-5)
x-5 = 2y - 10
x-2y = -10+5
x - 2y = -5 ... 1
In three years,
mark = x+3
Max = y+3
Now if Max's age will be 2/3 that of Mark, then;
x+3 = 2/3(y+3)
3(x+3) = 2(y+3)
3x + 9 = 2y+6
3x-2y = -3 .... 2
Solve 1 and 2 simultaneously
x - 2y = -5 ... 1
3x-2y = -3 .... 2
From 1: x = -5 + 2y
Substitute into 2:
3(-5+2y) - 2y = -3
-15 + 6y - 2y = -3
-15 + 4y = -3
4y = -3 + 15
4y = 12
y = 3
Recall thet x = -5+2y
x = -5+2(3)
x = -5 + 6
x = 1
The sum of their ages will be x+y
x+y = 1+3
x+y = 4
Hence the sum of their ages now is 4years
