SOLUTION: A sum of money was shared between Alvin, Zachary and Philip in the ratio 2:5:3 respectively. After Zachary spent 20% of his money, he had $196 less than the total amount of money t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A sum of money was shared between Alvin, Zachary and Philip in the ratio 2:5:3 respectively. After Zachary spent 20% of his money, he had $196 less than the total amount of money t      Log On


   

Question 540821: A sum of money was shared between Alvin, Zachary and Philip in the ratio 2:5:3 respectively. After Zachary spent 20% of his money, he had $196 less than the total amount of money that Alvin and Philip had. What was the total amount of money the three boys had in the beginning?
Answer by AnlytcPhil(1809) About Me  (Show Source):
You can put this solution on YOUR website!
The rule for dividing a number N into three parts in the ratio a:b:c is

1st part = a%2F%28a%2Bb%2Bc%29×N
2nd part = b%2F%28a%2Bb%2Bc%29×N
3rd part = c%2F%28a%2Bb%2Bc%29×N

Let the amount of money be $N

Alvin's part = 2%2F%282%2B5%2B3%29×N = 2%2F10×N = 1%2F5N
Zachary's part = 5%2F%282%2B5%2B3%29×N = 5%2F10×N = 1%2F2×N
Philip's part = 3%2F%282%2B5%2B3%29×N = 3%2F10×N = 3%2F10×N

>>...After Zachary spent 20% of his money, he had $196 less than the
total amount of money that Alvin and Philip had...<<
%28matrix%282%2C1%2C%22Zachary%27s%22%2C+part%29%29 - %28matrix%284%2C1%2C%2220%25%22%2C+of%2C+%22Zachary%27s%22%2C+part%29%29 =  - 196

  1%2F2N     - .20×1%2F2×N  =   (1%2F5N + 3%2F10N)     - 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