Question

A sum of money was shared between John and Joshua. John received 12/19 of the money and Joshua got the rest. After John spent 3/4 of his share, he found that he had $320 less than Joshua. Find the total sum of money they had at first.

Answer 1

John got 12/19 of money
Joshua got 7/19 of money

let John's amount be 12x
Josh's amount be 7x

John spent 3/4 of his, or he spent 9x
leaving him with 3x

Josh - John = 320
7x - 3x = 320
4x = 320
x = 80

so combined they had 19x = 1520

check:
John had 12x = 960
Josh had 7x = 560 , combined = 1520, check!
John spent 3/4 of his 960 or he spent 720 , leaving him with 240
which is 320 less than Josh's 560

All is good, my answer is correct

Answer 2

OR

x = sum of money

John received 12 / 19 of the money and Joshua got the rest means:

John received 12 x / 19 , Joshua got 7 x / 19

After John spent 3 / 4 of his share John will have 1 / 4 of his share = ( 12 x / 19 ) / 4

He found that he had $320 less than Joshua means:

( 12 x / 19 ) / 4 = 7 x / 19 - 320

12 x / 4 ∙19 = 7 x / 19 - 320

3 x / 19 = 7 x / 19 - 320

Add 320 to both sides

3 x / 19 + 320 = 7 x / 19

Subtract 3 x / 19 to both sides

320 = 4 x / 19

Multiply both sides by 19

6080 = 4 x

x = 6080 / 4

x = 1520

John received 12 x / 19 = 12 ∙ $1520 / 19 = $960

Joshua got 7 x / 19 = 7 ∙ $1520 / 19 = $560

Check result:

After John spent 3 / 4 of his share Joh will have rest of 1 / 4 of his share = 1 / 4 ∙ $960 = $240

Joshua's money - Rest of John's money = $560 - $240 = $320