The sum of the ages of Garfield Tom and Jerry is 85 years To

The sum of the ages of Garfield, Tom and Jerry is 85 years. Tom is twice as old as Jerry was 5 years ago. Five years from now, Garfield\'s age will be 2/3 the sum of the ages of Tom and Jerry at that time. How old are they?

Solution

Garfield - \'g\' ; Tom - \'t\' and Jerry \'j\'
Given g+ t + j = 85
t = 2( j-5)
g+5 = 2/3 ( t+5 + j +5)

We thus solve: t= 2j-10: - Equation A
3g+15 = 2t + 2j + 20 meaning 3g = 2t+2j +5
Put t= 2j-10 (from equation A) in this
3g = 2 (2j-10) + 2j + 5
3g = 6j -15 meaning g= 2j-5
t + g+ j =85
Thus (2j-10) + (2j-5) + j=85
5j -15=85
5j = 100 meaning j = 20
t = 2j-10 = 2*20-10 = 40-10 = 30 Thus t = 30
g = 2j-5 meaning 2*20 - 5 = 40-5 = 35 thus g = 35 years
Thus, at present, Tom is 30 years old Jerry is 20 years old and Garfield is 35 years old