Question 1077088
james invests 75000
gary invests 45000
the ratio of james investment to gary investment is 75/45= 15/9 = 5/3.
the profit is 480000 in the first year.
james share of the profit should equal 5/3 of gary share of the profit.


let a = james share of the profit.
let b = gary share of the profit.


a + b = 480000


a = 5/3 * b


equation of a + b = 480000 becomes 5/3 * b + b = 480000


multiply b by 3/3 to get 3/3 * b and the equation becomes 5/3 * b + 3/3 * b = 480000


combine terms with like denominators to get 8/3 * b = 480000.


solve for b to get b = 3/8 * 480000 = 180000


that's gary share.


james share is 480000 - 180000 = 300000


300000 / 480000 = .625 = 5/8 of the profits.


180000 / 480000 = .375 = 3/8 of the profits.


(5/8) / (3/8) = 5/8 * 8/3 = 5/3 which is the ratio of the investment of james to the investment of gary.


the general equation is:


let a + b equal the total investment.


the ratio of a to the total investment is a / (a + b)


the ratio of b to the total investment is b / (a + b)


the ratio of a to b is a / b


you were given the ratio of investment in the business was a to b, where a + b equaled the total investment.


the ratio of a to the total investment is therefore a / (a + b).


the ratio of b to the total investment is therefore b / (a + b)


bringing this to numbers, you get:


the ratio of james investment to gary investment is 5/3.


this means the ratio of james investment to total investment is 5 / (5 + 3) = 5 / 8


this means the ratio of gary investment to total investment is 3 / (5 + 3) = 3 / 8


therefore, the 480000 profit needs to be divided between james and gary in the ratio of 5 / 8 for james and 3 / 8 for gary.