The rule for dividing a number N into three parts in the ratio a:b:c is
1st part = ×N
2nd part = ×N
3rd part = ×N
Let the amount of money be $N
Alvin's part = ×N = ×N = N
Zachary's part = ×N = ×N = ×N
Philip's part = ×N = ×N = ×N
>>...After Zachary spent 20% of his money, he had $196 less than the
total amount of money that Alvin and Philip had...<<
- = - 196
N - ××N = (N + 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