"A secretary had to call all the clients of her company. By the morning she made 1/3 of the calls; in the afternoon she made 3/5 of the calls that were left and at night called the last 64 clients. With how many clients did she talk in the morning?" The answer is 80, but I really don't know how to get to it. I took it from a contest that happens in my country so, I had to translate the problem. One of the things that I tried was x = 1x/3 + 3x/5 + 64, but I got nowhere. This is driving me insane.
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2 Answers
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Let the total number of calls be $x$.
Morning: $\frac{1}{3}x$, afternoon: $\frac{3}{5}(x-\frac{1}{3}x)$ (because it is the left over ones), night:$64$.
So we have $x=\frac{1}{3}x+\frac{3}{5}(x-\frac{1}{3}x)+64$. Now solve for $x$, which should be $240$ and so the morning calls is $80$.
In short you got the afternoon one wrong because you were considering $\frac{3}{5}$ of the total call, not the left over ones.
answered Sep 19 at 18:14
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I like to work backwards. At the end, she called 64 clients. Just before that, she called ⅗ of those that were left, so 64 must have been ⅖ of those. So before the afternoon calls, there were 64 ÷ ⅖ = 160 clients. And before that, she called ⅓ of the clients, so 160 must have been ⅔ of those. So before the morning calls, there were 160 ÷ ⅔ = 240 clients. Now we're back at the beginning, so we know that she started with 240, and we can figure out anything else more straightforwardly. (In particular, the morning calls were ⅓ of 240, which is 80.)
