<PRE><B>Question 1206592</B>
.
Every month. Andie spent 1/5 of his salary on food and 
2/3 of the remaining salary on transport. 
After spending his salary on food and transport, he gave 50% of the rest of the salary to his parents 
and saved the rest of the $350 How much did he spend on food and transport every month?
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&lt;pre&gt;
Let x be the Andie&#39;s total salary.


               Make this table


    (line 1)   1/5 of x is spent on food.        The remainder is R1 = 4/5*x.

    (line 2)   2/3 of R1 is spent on transport.  The remainder is R2 = (1/3)*R1.

    (line 3)   0.5 of R2 is given to parents.    The remaining $350 go to saving.


Let&#39; start analyze from the last line 3.

From the table, from its line 3, the remainder of $350 for saving is the same amount as given to parents.

So, $350 is given to parents.

Thus R2 is twice $350, or $350 + $350 = $700.



Next, from the table, from its line 2,  R2 is 1/3 of R1.

R2 is $700, as we found out in line 3.  Hence,  R1 is 3 * $700 = $2100.

2/3 of R1 is 2/3 * 2100 = $1400.  It is the amount for transport.



Now let&#39;s analyze in line 1.

R1 is $2100, as we found out in line 2.

R1 is 4/5 of x.  Hence, x is 5/4*2100 = 2625 dollars and the spending on food is 1/5 * 2625 = 525 dollars.


Thus spending on food and transport together is $1400 + $525 = $1925.    &lt;U&gt;ANSWER&lt;/U&gt;


&lt;U&gt;CHECK&lt;/U&gt;.  Total salary is $2625.

        1/5 is spent on food,  1/5 * 2625 = 525 dollars. The remainder is R1 = $2625 - $525 = $2100.

        2/3 of R1 is spent on transport.  2/3 of $2100 is $1400,  The remainder R2 = $2100 - $1400 = $700.

        The remainder R2 = $700 is split evenly between parents and saving.  ! correct !
&lt;/pre&gt;

Solved.


---------------


I solved this problem using a backward method.


It allows restore unknowns step by step MENTALLY, moving backward 
from the end to the beginning, without using equations.


I consciously did not use the method of making and solving equations here,
since my goal was to make you familiar with this BACKWARD method.



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It is useful to know and to understand the following fact.


If your approach to solving the problem is making and solving equations, then the technical difficulties 
of constructing these equations will quickly increase with increasing the number of subdivisions
(of the length of the chain) in this problem.


But if your approach is a backward method, then it is almost the same, if the length of the chain 
is 5, or 10, or 20. The formal algorithm of the backward method remains the same, with no changes.


The backward method remains robust even for long chains of subdivisions (!)



</PRE>