MATH SOLVE

5 months ago

Q:
# 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 $, his investment in the second venture is $, and his investment in the third venture is $. NextReset

Accepted Solution

A:

x = first venture, y = second venture, z = third venture

x + y + z = 15,000

x + z = y + 7000

3x + 2y + 2z = 39,000

these are ur equations.....

x + y + z = 15,000

x - y + z = 7000

--------------------add

2x + 2z = 22,000

x + y + z = 15,000....multiply by -2

3x + 2y + 2z = 39,000

-------------------

-2x - 2y - 2z = - 30,000 (result of multiplying by -2)

3x + 2y + 2z = 39,000

------------------add

x = 9,000

2x + 2z = 22,000

2(9000) + 2z = 22000

18,000 + 2z = 22000

2z = 22000 - 18000

2z = 4000

z = 4000/2

z = 2,000

x + y + z = 15,000

9000 + y + 2000 = 15,000

11,000 + y = 15,000

y = 15,000 - 11,000

y = 4,000

first venture (x) = 9,000 <==

second venture (y) = 4,000 <==

third venture (z) = 2,000 <==

x + y + z = 15,000

x + z = y + 7000

3x + 2y + 2z = 39,000

these are ur equations.....

x + y + z = 15,000

x - y + z = 7000

--------------------add

2x + 2z = 22,000

x + y + z = 15,000....multiply by -2

3x + 2y + 2z = 39,000

-------------------

-2x - 2y - 2z = - 30,000 (result of multiplying by -2)

3x + 2y + 2z = 39,000

------------------add

x = 9,000

2x + 2z = 22,000

2(9000) + 2z = 22000

18,000 + 2z = 22000

2z = 22000 - 18000

2z = 4000

z = 4000/2

z = 2,000

x + y + z = 15,000

9000 + y + 2000 = 15,000

11,000 + y = 15,000

y = 15,000 - 11,000

y = 4,000

first venture (x) = 9,000 <==

second venture (y) = 4,000 <==

third venture (z) = 2,000 <==