Question 540821
<pre>
The rule for dividing a number N into three parts in the ratio a:b:c is

1st part = {{{a/(a+b+c)}}}×N
2nd part = {{{b/(a+b+c)}}}×N
3rd part = {{{c/(a+b+c)}}}×N

Let the amount of money be $N

Alvin's part = {{{2/(2+5+3)}}}×N = {{{2/10}}}×N = {{{1/5}}}N
Zachary's part = {{{5/(2+5+3)}}}×N = {{{5/10}}}×N = {{{1/2}}}×N
Philip's part = {{{3/(2+5+3)}}}×N = {{{3/10}}}×N = {{{3/10}}}×N
</pre>
>>...After Zachary spent 20% of his money, he had $196 less than the 
total amount of money that Alvin and Philip had...<<
<pre>
{{{(matrix(2,1,"Zachary's", part))}}} - {{{(matrix(4,1,"20%", of, "Zachary's", part))}}} = {{{((matrix(2,1,"Alvin's", part))+ (matrix(2,1,"Phillip's", part)))}}} - 196

  {{{1/2}}}N     - {{{.20}}}×{{{1/2}}}×N  =   ({{{1/5}}}N + {{{3/10}}}N)     - 196
 
(Can you solve that equation for N?  If not post again asking how.)

Solve that and get N = 1960, so they had $1960 total in the beginning.

You weren't asked how much each boy got, but you need to in order to 
check it:

Alvin got $392, Zachary got $980, and Phillip got $588.

Add them and get $1960. That checks. 

After Zachary spent 20% of his money, which means he spent 20% of his
$980, or $196, he had $784 left

That is supposed to be $196 less than the total amount of money that 
Alvin and Philip had.  Alvin and Philip together got $392 + $588 or $980.

And sure enough, $784 is $196 less than $980, since $980 - $196 = $784.

So $1960 is correct.

Edwin</pre>