SOLUTION: Santos is 84 years younger than Brooke. 6 years ago Brookes age was 4 times Santos age. How old is Santos now?

Question 1165624: Santos is 84 years younger than Brooke. 6 years ago Brookes age was 4 times Santos age. How old is Santos now?
Answer by mila nedic(19) (Show Source): You can put this solution on YOUR website!
Let's say that Santos's age will be represented by the letter s and Brooke's age will be represented by the letter b. We can use these variables to create equations that will help us solve the problem.
We have two pieces of information that we can use to create equations.
Santos is 84 years younger than Brooke: s+84=b
Six years ago Brooke's age was four times Santos's age: (s-6)*4=b-6
We now have two equations which will help us figure out the ages.
s+84=b and (s-6)*4=b-6
Since we know that s+84=b, we can use s+84 instead of b in (s-6)*4=b-6 so we are only dealing with one variable at a time.
(s-6)*4=b-6
(s-6)*4=(s+84)-6 (we replaced s+84 with b)
4s-6*4=s+84-6 (we removed the brackets)
4s-24=s+78 (the integers were simplified)
3s=102 (we subtracted s from both sides and added 24 to both sides to put the variable on one side and the integer on the other)
s=34 (we divided each side by three to isolate s)
Therefore Santos is 34 years old.

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