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.
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
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
To solve this problem, let's break it down into steps:
Step 1: Let's assume the total amount of money shared between John and Joshua is represented by 'x'.
So, John received 12/19 of 'x' = (12/19) * x.
That means Joshua received the rest of the money, which is (1 - 12/19) = (7/19) * x.
Step 2: After John spent 3/4 of his share, he had 1 - 3/4 = 1/4 of his share left.
So, John had (1/4) * (12/19) * x = (3/19) * x left.
Step 3: We are given that John had $320 less than Joshua.
Therefore, (3/19) * x = (7/19) * x - $320.
Step 4: Let's simplify the equation by multiplying both sides by 19 to get rid of the fraction:
3x = 7x - $6,080.
Step 5: Simplify the equation further by subtracting 7x from both sides:
3x - 7x = - $6,080.
-4x = - $6,080.
Step 6: Solve for x by dividing both sides by -4:
x = $6,080 / 4.
x = $1,520.
Therefore, the total sum of money they had at first was $1,520.