Three people Fatuma, Ali and Hassan contributed money to start a business.Fatuma contributed a quarter of the total amount and Ali two fifths of the remainder. Hassan’s contribution was one and a half times that of Fatuma. They borrowed the rest of the money from the bank which was $ 60,000 less than Hassan’s contribution, find the total amount required to start the business.
Fatuma ..1/4
Hassan .... 3/2 *1/4
Ali --- 2/5 of remainder
total amount invested ---- x
Fatuma's share = x/4
Ali's share = (2/5)(3x/4) = 3x/10
Hassan's share = (3/2)(x/4) = 3x/8
so far they have:
x/4 + 3x/10 + 3x/8
= 10x/40 + 9x/40 + 15x/40
= 37x/40
so they are still short 3x/40
3x/40 < 3x/8 by 60000
3x/40 = 3x/8 - 60000
-3x/10 = -60000
x = 200,000
check:
Fatuma's share = 50,000
Ali's share = (2/5)(150,000) = 60,000
Hassan = (3/2)(50,000) = 75,000
total so far = 185,000
short and borrowed from bank = 15,000
is 15000 less than 75,000 by 60,000 ?? , YES!
To find the total amount required to start the business, let's break down the contributions step by step.
1. Fatuma contributed a quarter (1/4) of the total amount required.
2. Let's denote the remaining amount after Fatuma's contribution as "x." So, the amount remaining after Fatuma's contribution would be (1 - 1/4) * x = 3/4 * x.
3. Ali contributed two fifths (2/5) of the remainder from step 2. So, Ali's contribution would be (2/5) * (3/4 * x) = 6/20 * x = 3/10 * x.
4. Hassan's contribution is one and a half (1.5) times that of Fatuma. So, Hassan's contribution would be 1.5 * 1/4 * x = 3/8 * x.
5. The remaining amount that needs to be borrowed from the bank is $60,000 less than Hassan's contribution. Therefore, the loan amount would be (3/8 * x) - $60,000.
To find the total amount required, we add up all the contributions:
Total amount required = Fatuma's contribution + Ali's contribution + Hassan's contribution + Loan amount
= 1/4 * x + 3/10 * x + 3/8 * x + [(3/8 * x) - $60,000]
Simplifying the equation further:
Total amount required = 1/4 * x + 3/10 * x + 3/8 * x + 3/8 * x - $60,000
To determine the exact value of x, we need more information or a given relationship between the contributions.