A math word problem?

Question

Can someone please help me write an equation and solve this math problem?

A group agrees to share equally in the cost of a $48,000 piece of machinery. If they could find two more group members, each member's share of the cost would decrease by $4000. How many are presently in the group?

Answer 1

Hi Smile,

let's say x = # of people in the group.

48000/x = y
48000/(x +2) = y - 4000

Now we substitute for y in the 2nd equation

48000/(x+2) = 48000/x - 4000

multiply by x*(x+2)
48000x = 48000(x+2) - 4000(x(x+2))

divide by 1000
48x = 48(x+2) - 4(x^2 + 2x)
48x = 48x + 96 - 4x^2 - 8x

subtract 48x
0 = 96 - 4x^2 - 8x
4x^2 + 8x - 96 = 0
x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0

solutions:
x = -6
x = 4

For this case, the answer must be non-negative, so
x = 4

Check:
48000/4 = 12000
48000/(4+2) = 48000/6 = 8000

12000 - 8000 = 4000

hth.

REgards,
Chas.

Answer 2

Let's call the present number in the group N.

So, the current price per share is 48000/N

The price per share with two more would be 48000/(N+2), which would be 4000 less.

Therefore, 48000/N - 48000/(N+2) = 4000

Divide through by 4000, to make it easier...

12/N - 12/(N+2) = 1

Multiply by N(N+2)...

12(N+2) - 12N = N(N+2)
12N + 24 - 12N = N^2 + 2N

Regroup...

0 = N^2 + 2N - 24

Factor the polynomial...

0 = (N + 6)(N - 4)

So N is either -6 or +4. Since a negative number of partners doesn't make sense, N = 4

Check: 48000/4 = 12000; 48000/6 = 8000; 12000 - 8000 = 4000.

Answer 3

I don't have an equation but, I randomly put in numbers. As of right now there are 4 members in the group. If you take $48,000 and divide it by 4 you'll have $12,000 per person. If you add 2 people and divide $48,000 by 6, you'll have $8,000 per person. The difference in $12,000 and $8,000 is $4,000.

Answer 4

The equation should be :

48000/x - 48000/(x+2) = 4000

Then solve for x and it will be the answer.

I think you should do the calculation for yourself.

Hope this help !!

Answer 5

48,000 / 4,000 = 12

so there are now 12 - 2 = 10