SOLUTION: Tony is half his father Simon's age. In 10 years, Tony will be three-fifths Simon's age. Ten years ago, Tony was one-third Simon's age. How old are Tony and Simon now? Please help

Question 832726: Tony is half his father Simon's age. In 10 years, Tony will be three-fifths Simon's age. Ten years ago, Tony was one-third Simon's age. How old are Tony and Simon now?
Please help I simply can not get my head around this
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be Simon's age, then x/2 is Tony's age
we are given x/2 +10 = 3(x+10) / 5 and
x/2 -10 = (x-10) / 3
either equation will give the same answer for x,
solve first equation equation for x
(x+20)/2 = (3x+30) / 5
cross multiply both fractions
5x +100 = 6x +60
x = 40
so Simon is 40 and Tony is 20
check our answers
10 years from now Simon is 50 and Tony is 30, so Tony is 30/50 or 3/5 Simon's age
10 years ago Simon is 30 and Tony is 10, so Tony is 10/30 or 1/3 Simon's age
answer checks :-)

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