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:
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.
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
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
Kk
48000/(x-4) -480000/x=20000
48000x-48000(x-4)=20000x(x-4)
Divide across with 20000
24x-24(x-4)=x(x-4)
X2-4x+96=0
X2+8x-12x+96=0
X(x+8)-12(x+8)=0
(X-12)(x+8)=0
Either x-12=0
48000x-48000(x-4)=20000x(x-4)
Divide across with 20000
24x-24(x-4)=x(x-4)
X2-4x+96=0
X2+8x-12x+96=0
X(x+8)-12(x+8)=0
(X-12)(x+8)=0
Either x-12=0
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