Question 260125: Carol Britz plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540. how many shares of each stock should she buy?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Carol Britz plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540. how many shares of each stock should she buy?
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Cost Equation: 32x + 23y = 10,100
Dividend Eq::: 1.20x+1.40y = 540
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Multiply thru the 2nd equation by 10 to get:
12x + 14y = 5400
32x + 23y = 10,100
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Multiply thru the 1st equation by 32
Multiply thru the 2nd equation by 12
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32*12x + 32*14y = 32*5400
12*32x + 12*23y = 12*10,100
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Subtract the 2nd from the 1st equation:
172y = 51600
y = 300 (# of $23 stocks to buy)
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Substitute into 12x + 14y = 5400 and solve for "x":
12x + 14*300 = 5400
12x = 1200
x = 100 (# of $32 stocks to buy)
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Cheers,
Stan H.
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