A certain amount of money is shared between Rui Feng and Vishal in th ratio of 5:9, if Rui Feng gets $44 less than Vishal, find the total amount of money that is shared between the two boys.
Let R = amount of money that Rui Feng has.
Let V = amount of money that Vishai has.
Then,
R:V = 5:9
or, R/V = 5/9
i.e. 9R = 5V
Also,
R = V - 44 (Rui Feng gets $44 less than Vishal)
9R = 9V - 396 (multiplying both sides by 9)
5V = 9V - 396 ( substituting for 9R = 5V)
4V = 396 ( rearrangement of equation)
V = 99
R = 55