Linda put an amount of money into each of two new investment

[bhavin30]

Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1 1/2 times that of investment A, what amount did Linda put into investment A

1. The interest for 1 year is $50 for investment A and $150 for investment B
2. The amount that Linda put into investment B is twice the amount that she put into investment A



OA - E, and I don't know why. Any help is really appreciated.

[Guest]

Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1 1/2 times that of investment A, what amount did Linda put into investment A

1. The interest for 1 year is $50 for investment A and $150 for investment B
2. The amount that Linda put into investment B is twice the amount that she put into investment A



OA - E, and I don't know why. Any help is really appreciated.

Interest of Rate of B = 1.5A
(Ex: 15 = 1.5 X X = 15/1.5 = 10

What is A?

Lets say: Investment 1 = K
Investment 2 = P


1) (K)A = 50
(P)B = 150

(K)B/1.5 = 50
(P)B = 150

(K)B = 75
(P)B = 150

2(K)B = (P)B

2K=P

TEST IT:
If investment K is $50 then investment P is $100
$50A=50
A=1

$100B = $150
We know B = 1.5 A
$100(1.5)1 = $150

This could work....lets try another one

Investment K = $500

$500A = 50

A = 50/500
A = 10%

Investment P = $1000
$1000B = 150
B=1.5A B = 1.5(.1) = 15%
$1000
$1000(.15) = $150

This one works too!

So we don't have a concrete investment amount because there are several different possibilities.




2) INSUFFICIENT: She could've put any amount of money into these investments and we cannot calculate and exact number with this type of uncertainty. This tells us the same info a statement 1

[RonPurewal]

try to think of these sorts of things in the abstract.

this advice may seem contradictory to some other advice we've given - specifically on number properties problems, on many of which we advise you to run around plugging in numbers all over the place right away - but it isn't: this problem, which features investments and interest rates, is much more conceptually accessible than are number properties problems dealing with such recondite concepts as differences of absolute values.
in general, on conceptually accessible problems (such as this one), you're better off accessing them conceptually, if at all possible.

--

let's take the 2 statements together, since the previous post has supplied decent reasons why the 2 individual statements are each insufficient.

thinking in the abstract, here's the problem: we have a RATIO of interest rates and a RATIO of initial principal investments, but we have no way to compute ACTUAL interest rates or principal investments.
another way of thinking about it: the interest rates could be, say, 0.02% and 0.03%, meaning that linda would have to invest a huge amount of money to accrue the given dollar amounts of interest. alternatively, the interest rates could be, say, 20% and 30%, meaning that linda would only have to invest nominal amounts of money.
therefore, still insufficient.

--

interestingly, if we have statement (1) plus the prompt, then statement (2) doesn't add any new information; in fact, we can deduce statement 2 from statement 1. here's how:
let the rate on A be r, and the rate on B be 1.5r.
let the principal on A be a, and the principal on B be b.
then ra = 50 and 1.5rb = 150.
the latter equation reduces to rb = 100.
therefore, since ra = 50 and rb = 100, it's clear that b is twice as big as a (either by dividing the equations, or just by inspection).

therefore, statements 1 and 2 together are the same as just statement 1 alone. since statement 1 is insufficient, both statements are still insufficient.

[luc2r4]

We know , I = principal * rate * time

In any of the Stements we were given the time they invested each,
( if we had the time, it would be possible to find Principal in both )

so 1 and 2 insufficient

St2 and St2 give the same information , then INSUFFICIENt

Please , let me know if it sounds logical.

[mschwrtz]

luc2r4, as Ron suggests you're smart to approach this problem at a fairly high level of abstraction. And certainly approaching it algebraically is more abstract than, for instance, plugging in numbers, but be careful here.

What you have shown is that interest, rate, and time taken together are sufficient to determine principal. You have not shown that no other information might be sufficient. Suppose that we knew the ratio of the interest on A to the interest on B, and the ratio of the time for A to the time for B, and the ratio of rate for A to the rate for B, and the actual principal for B. From this we could infer the principal for A without ever knowing any of A's interest, time, or rate.

[rachelhong2012]

use the

Quantity x average = sum table to work this problem out

Here, I'm showing the combination of two statements, assuming we already striked out A, B and D

here, quanttity= amount invested in A or B
average = interest rate for A or B
sum = interest earned from A or B

question: quantity for A =? Q =?
Q X A = SUM
A Q x A = 50
B 2Q x 1.5 A = 150
3 Q X ? = 200

QA = 50
3 QA = 150 or QA = 50

as you can see, we cannot solve for Q, because these two equations are essentially the same, hence E

[tim]

thanks for sharing..

[aliag916]

luc2r4, as Ron suggests you're smart to approach this problem at a fairly high level of abstraction. And certainly approaching it algebraically is more abstract than, for instance, plugging in numbers, but be careful here.

What you have shown is that interest, rate, and time taken together are sufficient to determine principal. You have not shown that no other information might be sufficient. Suppose that we knew the ratio of the interest on A to the interest on B, and the ratio of the time for A to the time for B, and the ratio of rate for A to the rate for B, and the actual principal for B. From this we could infer the principal for A without ever knowing any of A's interest, time, or rate.

Thanks for all the help in this question. So can we say: if the Interest amount, Principal investment, interest rate and time of Investment A is twice that of investment B and we are given the principal investment of B as $ 150, we can conclude that principal investment of A is $ 300 ie twice that of B ??

Thank u!

[RonPurewal]

if the Interest amount, Principal investment, interest rate and time of Investment A is twice that of investment B and we are given the principal investment of B as $ 150, we can conclude that principal investment of A is $ 300 ie twice that of B ??

Thank u!

I guess I don't understand your question. From the parts I highlighted in purple, it sounds as though your question is, "If the principal of investment A is twice the principal of investment B, then ... is the principal of investment A twice the principal of investment B?"

That's probably not what you're asking, so please clarify. Thanks.

[aliag916]

Hello, Sorry for that, let me rephrase using words of mschwrtz:

Suppose that we knew the ratio of the interest on A to the interest on B is 2:1, and the ratio of the time for A to the time for B is 2:1, and the ratio of rate for A to the rate for B is 2:1, and the actual principal for B is 100. The ratio of principal of A to Principal of B is also 2:1. From this how could we infer the principal for A without ever knowing any of A's interest, time, or rate?

Thank you!

This is how I solved it, please let me know if I did it correctly:
I get Principal for A = 400

For B, let the Principal, interest amount, interest rate and time be P, IntB, R and T respectively so I get :
IntB = PRT
Then Simple interest on A would be :
2IntB = 2P*2R*2T or
Int B = 4PRT so I get the answer that Principal for A will be 4 times that of B (100) ie 400

[RonPurewal]

Hello, Sorry for that, let me rephrase using words of mschwrtz:

Suppose that we knew the ratio of the interest on A to the interest on B is 2:1, and the ratio of the time for A to the time for B is 2:1, and the ratio of rate for A to the rate for B is 2:1, and the actual principal for B is 100. The ratio of principal of A to Principal of B is also 2:1. From this how could we infer the principal for A without ever knowing any of A's interest, time, or rate?

Are the two red things supposed to be different?

[aliag916]

Yes, interest is the actual amount ($)of interest earned and rate is the rate of interest in percent. Sorry for the confusion. I myself don't like interest questions much so trying to clarify my doubts.

thanks a lot!

[RonPurewal]

Yes, interest is the actual amount ($)of interest earned and rate is the rate of interest in percent. Sorry for the confusion. I myself don't like interest questions much so trying to clarify my doubts.

thanks a lot!

If that's what you mean, then the above situation is impossible. If A starts with twice as much principal as B, and earns twice as much % interest for twice as long, then, with simple interest, A will earn 8 times as much interest as B. (With compound interest, A will earn slightly more than 8 times as much interest.)
Just plug in some specific values if you don't immediately see why.