Question

marvin invested $6000 more at 5% than he invested at 8%. his total income was $2420 . how much did he investe at each rate? i know that Interest = principal * rate* time.
is this question solvable, since time is not given?
if t = 1, then its solvable, and i got the the amount invested at 8% is 16307.76

Answer 1

i get x = amount invested at 5
y = amount invested at 8%

.05 ( 6000 + y) + .08y = 2420

Answer 2

but dont we need to take time into account here

Answer 3

the interest accumulated on left = total interest on right

Answer 4

so it should be
.05 ( 6000 + y)*t + .08y*t = 2420 , where 2420 has the time built in

Answer 5

.05 ( 6000 + y) + .08y = 2420

thats correct

Answer 6

they really should tell you the time period, but since its not given you just assume a year ( or however long it takes to get 8% interest )

Answer 7

He invested P dollars at 8% for t years and got a return of 0.08Pt dollars.

Then he invested P + 6000 dollars at 5% interest for t years and got a
return of (0.05P + 300)t dollars.

So his total income is (0.05P + 300)t + 0.08Pt = 2420

Without knowing how long the investment lasted, we can't tell the amount
he originally invested.

Answer 8

elecengineer, 8 percent is given initially , so

Answer 9

what do you mean, how long it takes to get 8 percent interest

Answer 10

just one time period

Answer 11

i think the interest rate is stipulated

Answer 12

if the answer says he earns 8% then that means it was in the bank for long enough to earn 8% , if that makes sense.

Answer 13

no all they are saying is that there is a certain period of time , over which one investment gets 8% and the other 5%

Answer 14

actually time is not really mentioned

Answer 15

but i guess in these types of problems, we just assume time is year, since it isnt given

Answer 16

which is why you assume , they wouldnt mark it down it wasnt specified , but you dont actually need to the know actual time to answer the question anyway

Answer 17

because both investments are for the same time, it has no effect

Answer 18

no, read what he said, james

Answer 19

He invested P dollars at 8% for t years and got a return of 0.08Pt dollars.

Then he invested P + 6000 dollars at 5% interest for t years and got a
return of (0.05P + 300)t dollars.

So his total income is (0.05P + 300)t + 0.08Pt = 2420

Without knowing how long the investment lasted, we can't tell the amount
he originally invested.

Answer 20

james i agree, two unknowns , cant solve

Answer 21

elecengineer, i think the time does have an effect.

Answer 22

these problems though are ubiqutous in baby algebra books. a system of equations, something in terms of rate and total. except we get this problem in this case

Answer 23

i say baby algebra, to distinguish from algebra (group theory , rings, fields, )

Answer 24

you can find the original amount invested P in terms of t (which is in years):

P = (2420 - 300t)/0.13t

and hence get an upper bound on t:

t <= 8.0667 years

Answer 25

how>?

Answer 26

because he invested a non-negative amount of money

Answer 27

oh , so youre looking at that function

Answer 28

y = (2420 - 300x)/(0.13x)

Answer 29

x>0 and y> 0

Answer 30

wait, P goes to infinity as t approaches zero