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

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.