I am trying to solve the following problem (from this book).
I have tried several ways using fractions and proportions with no success. I really miss the point here, and I am not able to logically solve it.
I kindly ask you if you could provide me some tips/guidelines/steps how to solve it, I really would like to understand the logic behind the solution.
The problem:
A man divides 1622,50 EUR among four persons so that the first has 40 EUR more that the second, the second 60 EUR more then the third, and the third 87.50 EUR more than the fourth. How much did the fourth person receive? The solution is 300 EUR.
In case this question is not appropriate here, please let me know I can move it to different stack exchange site.
You can create linear equations for these
Let $a, b, c, d$ be the amounts that these four people have respectively. Now,
$$c = d + 87.50$$ $$b = c + 60$$ $$b = d + 87.50 + 60$$ $$a = b + 40$$ $$a = d + 87.50 + 60 + 40$$ $$a + b + c + d = 1622.50$$ $$d + 87.50 + 60 + 40 + d + 87.50 + 60 + d + 87.50 + d = 1622.50$$ $$ 4d + 422.5 = 1622.5 $$ $$ 4d = 1200 $$ $$ d = 300 $$