the sum of the ages of sam and tomas is 27 years. seven years ago, tomas was three years more than one-fourth as old as sam. find their present age

Answer 1

Let Sam's age 7 years ago be s
let Tom's age 7 years ago be t

So
s+7 + t+7 = 27
s+t = 13 ---> t = 13-s

"seven years ago, tomas was three years more than one-fourth as old as sam"
--- t = (1/4)s + 3
13-s = (1/4)s + 3
times 4
52 - 4s = s + 12
-5s = -40
s = 8

so 7 years ago Sam was 8 and Tom was 5

So NOW they are 15 and 12

Check :
is the sum of their present ages 27
15+12 = 27 , check!

7 years ago, is Tom 3 more than 1/4 of Sam's age
1/4 of Sam= 2
3 more than that is 5, which was Tom's age, check!!