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 \cdot p n \cdot p = (n - 4) \cdot (p + 20000) n \cdot p = n \cdot p - 4 \cdot p + 20000 \cdot n - 4 \cdot 20000 4 \cdot 20000 = 20000 \cdot n - 4 p 4 \cdot 20000 = 20000 \cdot n - 4 \cdot (480000 / n) 4 \cdot 20000 \cdot n = 20000 \cdot n^{2} - 4 \cdot 480000 4 \cdot 20000 \cdot n = 20000 \cdot n^{2} - 4 \cdot 480000 - 20000 n^{2} + 80000 n + 1920000 = 0 20000 n^{2} - 80000 n - 1920000 = 0 20000 = 2^{5} \cdot 5^{4} 80000 = 2^{7} \cdot 5^{4} 1920000 = 2^{10} \cdot 3 \cdot 5^{4} GCD (20000, 80000, 1920000) = 2^{5} \cdot 5^{4} = 20000 n^{2} - 4 n - 96 = 0 a = 1; b = - 4; c = - 96 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 96) = 400 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 4 0 0}{2} n_{1, 2} = \frac{4 \pm 2 0}{2} n_{1, 2} = 2 \pm 10 n_{1} = 12 n_{2} = - 8 n = n_{1} = 12 Verifying Solution: p = 480000 / n = 480000 / 12 = 40000 ksh t_{1} = n \cdot p = 12 \cdot 40000 = 480000 ksh t_{2} = (n - 4) \cdot (p + 20000) = (12 - 4) \cdot (40000 + 20000) = 480000 ksh t_{1} = t_{2}

Our quadratic equation calculator calculates it.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

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.

1 year ago Like

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

1 year ago 3 Likes Like

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

1 year ago 3 Likes Like

Or x+8=0
Since x cannot be -ve then original number of men is
X=12

1 year ago 2 Likes Like

Tips for related online calculators

Are you looking for help with calculating roots of a quadratic equation?
Check out our ratio calculator.
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?

A group

Correct answer:

Step-by-step explanation:

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

Related math problems and questions: