Question 1106533: 5 years ago Sara's aunt was 4 times as old as Sara. If Sara's aunt is 42 years older than Sara, how old is Sara now? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52775) (Show Source):
A -5 = 4*(S-5), (1) ("5 years ago . . . ")
A = S + 42. (2) ("At present time . . . ")
From (2), substitute the expression for A into (1). You will get
(S + 42) - 5 = 4*(S-5),
S + 37 = 4S - 20 ====> 37 + 20 = 4S - S ====> 57 = 3S ====> S = = 19.
Answer. Sara is 19 years old.
The difference between their ages is 42 years. In particular, when Sara's aunt was 4 times as old as Sara, the difference in their ages was 42 years. 42 years older and 4 times as old means their ages were 14 and 56.
Note: you might be able to figure that out using logical reasoning; if you want to see it algebraically, it might look like this: [the difference between the ages of Sara's aunt, who is 4 times as old as Sara, and Sara, is 42]
So when Sara's aunt was 4 times as old as Sara, their ages were x=14 and 4x=56.
Since that was 5 years ago, Sara's age now is 14+5 = 19.
