Question 74156: Joe Student wins the lottery! Being a loyal Northwesterner he decides to invest his $13,000 in local companies. He invests part of the principal in Starbuck's stock which gains 7% in value and, sadly, the rest of his winnings on Boeing stock which loses 10% of it's value in one year. At the end of the year Joe's stock has gained $60 in value. How much did he invest in each company?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 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
.
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:
.
0.07S - 0.10B = 60
.
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
.
Substitute the right side of this equation for S into the return equation as follows:
.
7S - 10B = 6000
.
7(13000 - B) - 10B = 6000
.
Multiply out to get:
.
91000 - 7B - 10B = 6000
.
Combine the two terms containing B
.
91000 - 17B = 6000
.
Get rid of the 91000 on the left side by subtracting 91000 from both sides to obtain:
.
-17B = -85,000
.
Divide both sides by -17 to find B
.
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.
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