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Last year Mrs. Long received $160 in dividends on her shares of Compan

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Bunuel
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Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink] New post   31 May 2022, 03:15
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Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

(A) 128
(B) 140
(C) 172
(D) 175
(E) 200
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JerryAtDreamScore
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Re: Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink] New post   31 May 2022, 15:42
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Bunuel wrote:
Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

(A) 128
(B) 140
(C) 172
(D) 175
(E) 200


Breaking Down the Info:

$15 relative to $160 is \(\frac{15}{160} = \frac{3}{32}\) more. Then 12 more stocks is also \(\frac{3}{32}\) more stocks.

Thus there must be \(12 * \frac{32}{3} = 128\) stocks originally.

Answer: A
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Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink] New post   30 Jun 2023, 23:51
JerryAtDreamScore wrote:
Bunuel wrote:
Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

(A) 128
(B) 140
(C) 172
(D) 175
(E) 200


Breaking Down the Info:

$15 relative to $160 is \(\frac{15}{160} = \frac{3}{32}\) more. Then 12 more stocks is also \(\frac{3}{32}\) more stocks.

Thus there must be \(12 * \frac{32}{3} = 128\) stocks originally.


Answer: A


I quite liked this approach but I am having issue grasping the concept. I did get the correct answer by setting up the equations but can anyone elaborate on this with a little more detail?
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LucienH
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Re: Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink] New post   31 Oct 2023, 17:39
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What I did is first finding the dividend per share:
15/12 is the dividend per share (as 12 more shares result in an additional 15$ in total dividends)

thus I set up the equation where X is the original amount of shares:
160 + 15 = (X+12)*15/12
X = 128
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Re: Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink] New post   09 Nov 2023, 10:38
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I had another method. I will explain.

The share to dividend ratio is 12:15 (which is equal to 4:5)
Step 1: go from 4:5 to S:160 with S the number of shares you're looking for.
Step 2: to go from 5 to 160 you multiply 5 by 32 (160/5=32).
Step 3: multiply 4 by 32 = 128
Final ratio: 128:160
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Re: Last year Mrs. Long received $160 in dividends on her shares of Compan [#permalink]
09 Nov 2023, 10:38
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