Question 74156
Call Joe's investment in Starbuck's S and Joe's investment in Boeing B. Since we know the two
investments total $13,000 we can write the equation:
.
S + B = 13000
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We also know that Joe's investment in Starbuck's gains 7% in value and his investment in
Boeing loses 10% and if we total the two investments the answer is $60.  Using decimals for
percents this becomes in equation form:
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0.07S - 0.10B = 60
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Multiply this equation (all terms) by 100 to eliminate the decimals and get:
.
7S - 10B = 6000
.
Return to our first equation and solve it for one of the variables in terms of the other.
For example, solve for S by subtracting B from both sides to get:
.
S = 13000 - B
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Substitute the right side of this equation for S into the return equation as follows:
.
7S - 10B = 6000
.
7(13000 - B) - 10B = 6000
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Multiply out to get:
.
91000 - 7B - 10B = 6000
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Combine the two terms containing B
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91000 - 17B = 6000
.
Get rid of the 91000 on the left side by subtracting 91000 from both sides to obtain:
.
-17B = -85,000
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Divide both sides by -17 to find B
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B = (-85000/-17) = 5000
.
So we know that Joe had $5,000 invested in Boeing Stock.  Since he invested $13,000 total
the remaining $8,000 was invested in Starbuck's.
.
Hope this helps you to understand this problem and the need for two separate equations
to solve for the two variables.