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?  Choices: A) 128 B) 140 C) 172 D) 175 E) 200
A   1. Realize that if there were 12 more shares and 15 more dollars, the shares are worth more than a dollar a share, so there would have to be less than 160. Cancel out c, d, e.   2. Now there are at least three ways of doing it, all of which depend on who you are and how you think. I'll put as many below as I can think of - I think they're all fine and expediant. Remember - if you're spending time looking for the most sophisticated way, you could be just wasting time, especially if you know how to do it algebraically.   Method 1: Algebra   160/x = 175/(x+12)   That's because each stock is worth the same, so if you divide the 160 by the number of shares, or 175 by the number of shares plus 12, you get the same answer. Solve for x = 128.   Method 2: 12 more shares cost $15, so that means each one cost $1.25. So 160/1.25. To do this quickly, convert 1.25 into 5/4(I LOVE FRACTIONS!)Now you've got 160/(5/4) = 160x4/5 = 32x4 = 128.   answer is 128
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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?