4 ms·
Ann is 18. I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some poi
by HarHarVeryFunny 3mo ago
Ann is 18.
I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some point in the past "when Mary was as old as Ann is now" (M' & A').
So, what we're given is:
M = 24
M' = A
M = 2A' => A' = M/2 = 12
Since the age gap between Mary and Ann is constant, we know:
M - A = M'- A'
So, substituting in the known values:
24 - A = A - 12
2A = 36
A = 18
We can double check the result. Since Mary (24) is 6 years older than Ann (18), then when Mary was 18 Ann would have been 12, so Mary is now twice that age as given.
- bayesnet 3mo agoI think it’s easier to see if you drop the time indices and just introduce a variable for the elapsed time. So: Mary := 24 = 2(A - Δ) A = Mary - Δ And then it’s just substitution. But of course what appeals to one’s intuition is very personal
- HarHarVeryFunny 3mo agoTo me, explicitly representing the two pairs of ages (now: M, A; previously: M', A') is simpler because it let's you directly represent the problem statement without any mental gymnastics whatsoever. M = 2A' "Mary is [now] twice as old as Ann was ..." M'= A "when Mary was as old as Ann is now"
- m_herrlich 3mo agoThanks for sharing this, it actually makes it easy. I somehow convinced myself it was a trick having to do with ages being rounded off to whole numbers, so delta-age can be off by one... anyway I want my day back.