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Question 1077088: James and Gary decide to open a business together. James invests R 75 000 and Gary invests R 45 000. They agree to divide any profits in the same ratio as their initial investments. The business shows a profit of R 480 000 in the first year.
4.1.1 Express the ratio of the initial investments in simplified form. (2)
4.1.2 How much does James and Gary get in profits in the first year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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