# Average investment

1. Mar 21, 2016

### Natasha1

1. The problem statement, all variables and given/known data

A large company insists that each shareholder invests at least £12,000 in the company. At present, the company has two thousand shareholders and their average investment is £13,040.

1. How much is their total investment?

2. Suppose that 100 new people become shareholders in the company. What is the lowest level to which the average investment could drop? Give your answer to the nearest pound.

3. In fact a further n new people become shareholders and on average they invest £12,320. If the average investment across all the shareholders is now £12,960, find n.

2. Relevant equations and attempt at a solution
1. I did:

2000 x 13,040 = £26,080,000 (is this correct please?)

2. I did:

100 x 12,000 = £1,200,000 (total minimum investment from these 100 new shareholders)
Therefore,

£1,200,000 + £26,080,000 = £27,280,000 (is this correct please?)

3. I did:

n x 12,320 = £12,320n (total investment from these n new shareholders)
(2000+n) x £12,960 (total investment from all the shareholders old and new)

What do I need to do now? I'm stuck??

2. Mar 21, 2016

### SteamKing

Staff Emeritus
This is correct.

That's not what the question is asking for.

What is the lowest level to which the average investment could drop? [After these 100 people have invested.]
You need to account for the total investment made by the older shareholders, before this group of n invested.

3. Mar 21, 2016

### Natasha1

2. Is it:

100 x 12,000 = £1,200,000 (total minimum investment from these 100 new shareholders)
Therefore,

£1,200,000 + £26,080,000 = £27,280,000 / 2100 = £12,990 per person (is this correct?)

4. Mar 21, 2016

### SteamKing

Staff Emeritus
Yes.

5. Mar 21, 2016

### Natasha1

Could you start me off please SteamKing I'm stuck

6. Mar 21, 2016

### SteamKing

Staff Emeritus
n new investors have invested an average of £12,320 each. After this pile of money is invested, each shareholder has an average of £12,960 invested. Find n, the number of new investors. To do this, you need to account for the original amount invested by the original investors.

7. Mar 21, 2016

### Natasha1

2000 x 13,040 = £26,080,000 is the total invested by the older shareholders

so £26,080,000/2000 = £13,040
£27,280,000/x = £12,960
so x = 2105 hence 105 new shareholders (is this correct?)

8. Mar 21, 2016

### SteamKing

Staff Emeritus
Well, you can check your answer against what is happening to the investments to see if you get the overall average investment after the new group has contributed.

It's best to set up each average investment in algebraic terms and then equate the two.

It's already been established that the original 2000 investors have contributed an aggregate of £26,080,000. We don't know what the total investment is after the n new investors have contributed; we only know what the average investment is when it is spread out over 2000+n people.

9. Mar 22, 2016

### Natasha1

(2000+n)x12,960 = £12,320n + £26,080,000
25,920,000 + 12,960n = £12,320n + £26,080,000
640n = 26,080,000 - 25,920,000
640n = 160,000
n = 250 (is this correct?)

10. Mar 22, 2016

### SteamKing

Staff Emeritus
Why yes, it does appear to be correct.