A group

A group of young men decides to raise ksh 480,000 to start a business. Before the actual payment was made, four members pulled out, and each of the remaining had to pay an additional ksh 20,000. Determine the original number of members.

Correct answer:

n =  12

Step-by-step explanation:

480000= n p n p = (n4) (p+20000)  n p = n p 4 p+20000 n4 20000 4 20000 = 20000 n  4p  4 20000 = 20000 n  4 (480000/n)  4 20000 n=20000 n24 480000  4 20000 n=20000 n24 480000 20000n2+80000n+1920000=0 20000n280000n1920000=0 20000=2554 80000=2754 1920000=210354 GCD(20000,80000,1920000)=2554=20000  n24n96=0  a=1;b=4;c=96 D=b24ac=4241(96)=400 D>0  n1,2=2ab±D=24±400 n1,2=24±20 n1,2=2±10 n1=12 n2=8  n=n1=12   Verifying Solution:  p=480000/n=480000/12=40000 ksh t1=n p=12 40000=480000 ksh t2=(n4) (p+20000)=(124) (40000+20000)=480000 ksh  t1=t2

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Showing 4 comments:
Math student
I see that you used a different method to solve the equation. You factored out the common factor of 20000 and then used the quadratic formula to find the roots. That’s a valid approach.👏

However, I noticed that you made a mistake in the last step. You wrote n=n 1​=12, but n 1​=2+10=12 is not a solution of the equation. If you plug in n=12 into the equation, you get:

120 = 122 - 5*12

120 = 144 - 60

120 ≠ 84

So n=12 is an extraneous root that does not satisfy the original equation. The only solution that works is n=n 2​=2-10=-8. But since n must be a positive integer, we reject this solution as well. Therefore, there is no solution to the equation using your method.

Math student
my solution is:
Let x be the original number of members. Then the original amount each member had to pay is 480,000/x. When four members pulled out, the remaining members had to pay 480,000/(x-4). The difference between these two amounts is 20,000. So we can write the equation:

480,000/x - 480,000/(x-4) = 20,000

To solve this equation, we need to multiply both sides by x(x-4) and simplify:

480,000(x-4) - 480,000x = 20,000x(x-4)

Expanding and collecting like terms, we get:

-1,920,000 = -16,000x2 + 80,000x

Dividing both sides by -16,000, we get:

120 = x2 - 5x

Adding 25 to both sides and completing the square, we get:

145 = (x-2.5)2

Taking the square root of both sides, we get:

x-2.5 = ±√145

Adding 2.5 to both sides, we get:

x = 2.5 ±√145

Since x must be a positive integer, we reject the negative root and get:

x = 2.5 +√145

Rounding to the nearest whole number, we get:

x = 14

Therefore, the original number of members was 14

48000/(x-4) -480000/x=20000
Divide across with 20000
Either x-12=0

Or x+8=0
Since x cannot be -ve then original number of men is

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