Question 1180260: Jake has decided to invest in three business ventures. The total cost of investing in all three ventures is $15,000. The combined investment in the first and third ventures is $7,000 more than the investment in the second venture. According to Jake's research, his investment in the first venture will triple after three years, and the investments in the other two ventures will double in the same period, making the total value of his investment $39,000.
Jake's investment in the first venture is $?
a. $6,000
b. $8,000
c. $9,000
d. $10,000
His investment in the second venture is $?
a. $2,000
b. $4,000
c. $6,000
d. $7,000
And his investment in the third venture is $?
a. $1,000
b. $2,000
c. $3,000
d. $4,000
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
Jake has decided to invest in three business ventures. The total cost of investing in all three ventures is $15,000. The combined investment in the first and third ventures is $7,000 more than the investment in the second venture. According to Jake's research, his investment in the first venture will triple after three years, and the investments in the other two ventures will double in the same period, making the total value of his investment $39,000.
Let x,y,z be the investment in I , II, and III investment respectively
x+y+z=15000 ----------------(1)
x+z = y+7000 ----------------(2)
x-y+z =7000 ----------------(3)
3x +2y+2z =39000 -------------(4)
Add 1&3
2x+2z=22000
x+z = 11000
plug x+z in (2)
x+z = y+7000
11000 =y+7000
y = 4000----------------II
multiply (1) b7 2 and subtract (4)
x+y+z=15000
2x+2y+2z =30000
3x +2y+2z =39000
----------------
-x = -9000
x=9000----------------------I
z = 2000--------------------III
First venture $9,000
Second venture $4000
Third venture $ 2000
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