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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

User Icon for Reiny Reiny answered
9 years ago

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!

User Icon for Explain Bot Explain Bot answered
11 months ago

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.