Question

Linda invest 25000 for one year part is invested at 5% another part at 6% and the rest at 8%. the total income from all three investments is $1600. the income from the 5% and 6% investments is the same as the income from the 8% investment. find the amount invested at each rate.

Answer 1

Total Invested Amount = $25,000

Total Income from investment through 3 parts = $1600

So, (Income from 5% part ) + ( Income from 6% part) + Income from 8 % part = $1600.....................( i )

and given is,.  (Income from 5% part ) .+ .( Income from 6% part) .= Income from 8 % part...............( ii )

Substituting ( ii ) in ( i )  we get :-

Income from 8% part. +. Income from 8% part .= $1600

Therefore Income from 8% part = $ 1600 ÷ 2 .= $800

Income from 8% part is $800

If 8% = $800

Then 1% = $800 ÷ 8 = $100

Hence 100% (Total Amount) = $100 × 100 = $10,000

So, Amount invested in 8% part is $10,000

Now,

Amount leftover = $25,000 - $10,000 = $15,000

Let Amount invested in 5% part = x

and Amount invested in 6% part = $15,000 - x

Income from X at 5% is = 5% of x = 5/100 * x = 0.05x

Income from 15000 - x part at 6% is = 6% of $15000 - x = 6/100 * $15,000 - x = 0.06*(15,000 - x)

As we know total income from both these is equal to Income from 8% part = $ 800

So Using the fact

0.05x + 0.06 (15000 - x) = 800

0.05x + 900 - 0.06x = 800

​​​​​​900 - 800 =. 0.06x - 0.05x

100 = 0.01x

x = 100 ÷ 0.01. = 10,000

Hence the part at 5% rate is $10,000

and the part at rate 6% is ($15,000 - $10,000) = $5,000

So part invested at 6% is $5000

Therefore all the three parts are

1^st part at 5% is​​​​​ $ 10,000

2^nd part at 6% is $ 5,000

3^rd part at 8% is $ 10,000.

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