Emma's uncle is 3434 years older than she is. In 77 years' time, her uncle will be triple Emma's age. How old is Emma's uncle now?
Question
Emma's uncle is 3434 years older than she is. In 77 years' time, her uncle will be triple Emma's age. How old is Emma's uncle now?
Solution
Let's denote Emma's current age as E and her uncle's current age as U.
From the problem, we know two things:
-
U = E + 34 (Emma's uncle is 34 years older than she is)
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U + 7 = 3 * (E + 7) (In 7 years, her uncle will be triple Emma's age)
We can substitute the first equation into the second to solve for E:
(E + 34) + 7 = 3 * (E + 7)
This simplifies to:
E + 41 = 3E + 21
Subtract E from both sides:
41 = 2E + 21
Subtract 21 from both sides:
20 = 2E
Divide both sides by 2:
E = 10
Substitute E = 10 into the first equation to find U:
U = 10 + 34 = 44
So, Emma's uncle is currently 44 years old.
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