SOLUTION: 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?

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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(52776)   (Show Source): You can put this solution on YOUR website!
.
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.

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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


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.
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