Question

how much should be invested at 10% if one has $5000 to invest, in order that the annual income from one investment at 10% shall double the income from another investment at 15%?

Answer 1

They don't say, but let's assume this is simple interest, so the annual income is the interest:
Interest Rate * Principal

they question seems to be asking: if you divide 5000 into 2 parts (call them x and y)
then the interest on the x part (at 10%) is twice as big as the interest on the y part (invested at 15%)

here is what you have:
x+y= 5000 (the sum of the two chunks of money is 5000)

10% of x = 2*(15% of y)

can you solve this ?

Answer 2

I dont get it :(

Answer 3

what is the interest you get from 5000 at 10% ?

Answer 4

500

Answer 5

yes 0.10*5000=500

but if you put all of the 5000 in at 10% there is none left over to invest at 15%
the interest you get on the amount invested at 15% is 0 (because we invested nothing)

if we invested half the money at 10% and half at 15% we would get
0.10*2500 = 250
0.15*2500 = 375

but the question says we want
** one investment at 10% shall double the income from another investment at 15%?**

in other words they want
the interest from 0.10 more (twice as much) as the interest from the 0.15

Answer 6

you could try "trial and error" and keep putting more and more into 10% and the amount left over into 15%, and compare the amount of interest.

for example
0.10*4000= 400
0.15*1000= 150

now 400 is more than twice as much as the 150, so 4000 is too much to put in the 10%

Answer 7

but you can use algebra to solve this:
let x be the amount to put into 10%
how much is left over for the 15% ? we start with 5000, take away x, what is left ?
5000-x

so we could say
0.10*x = some amount = A
0.15*(5000-x) = 1/2 as much = A/2
(call the amount of interest A)
if you double the interest from the 15%
2* 0.15*(5000-x) = 2*A/2 = A it will match the interest from 10%

set them equal:
2* 0.15*(5000-x) = 0.10*x

now simplify and solve for x