A school must raise exactly $2,500 over the next year by investing a

Could you please elaborate your approach?

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The school must raise exactly $2,500 by investing as much as possible in stocks.
I have assumed that amount to be x.

Investment in stocks yields 9% therefore the returns from this investment = 9x/100

The remaining amount i.e. (30000-x) is invested in bonds, which yield 8% annual interest. i.e. (8/100)*(30000-x)

The sum of the returns from both investments = 2500. So,

9x/100 + (8/100)*(30000-x) = 2500
x = 10000

therefore the school must invest 10000 in stocks to raise exactly $2,500 by investing as much as possible in stocks.

appu2693 : Hope its clear
Hit Kudos if you liked it

2,500 = a/100 * 30,000
2,500/300 = a
8.33 = a, this is the interest we need get 2,500 from 30,000

1) Draw a number line:

8---8.3------9
B---Avg------S

We have 2 amounts, bonds at at 8% and stocks at 9% interest
If it was exactly half of each, it would be 8.5% ... while we have a = 8.3%
The distance from 8 to 9 is 1, so we can say the ratio of the 'pull' of bonds on the average is 2/3 to the 'pull' of stocks at 1/3, or a ratio of 2:1. Since we're looking for stocks it would be 30,000 * 1/3 = 10,000


Or 2) Use weighted average formula:
w1/w2 = Avg2 - Avg / Avg - Avg1
Bonds/Stocks = 90 - 83 / 83 - 80
B/S = 7/3
so S = 3/10 * 30,000 = 9,000 (due to rounding... closest answer is B)

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