Posted by Shawna on Wednesday, March 19, 2014 at 10:26am.
Jake has decided upon three business ventures to invest in. The total cost of investing in all three ventures will be $15,000. Investing in the first venture will cost $3,000 more than investing in both the second and the third venture. According to Jake’s research, his investment in the first venture will triple after three months, and the investments in the other two ventures will double in the same period, taking the total valuation of his investments to $30,000. What is the investment Jake will be making for each of these three ventures?
A) first venture: $9,000
second venture: $4,000
third venture: $2,000
B) first venture: $9,000
second venture: $2,000
third venture: $4,000
C) first venture: $8,000
second venture: $3,500
third venture: $3,500
D) first venture: $10,000
second venture: $4,000
third venture: $1,000
E) first venture: $8,000
second venture: $3,000
third venture: $1,000

Math  clarify  Steve, Wednesday, March 19, 2014 at 10:57am
When you say
Investing in the first venture will cost $3,000 more than investing in both the second and the third venture.
do you mean #1 is 3000 more than both #2 and #3 combined, or 3000 more than either #2 or #3?

Math  PreCalc (12th Grade)  Shawna, Wednesday, March 19, 2014 at 11:09am
I believe combined.

Math  PreCalc (12th Grade)  Shawna, Wednesday, March 19, 2014 at 11:12am
As explained , C, D and E cannot be correct.
A + B + C = 15000
A = B + C + 3000
3A + 2B + 2C = 30000
Solve these equations to get A, B and C

Math  PreCalc (12th Grade)  Steve, Wednesday, March 19, 2014 at 11:20am
ok. so we have
x + y + z = 15000
x = y + z + 3000
3x + 2y + 2z = 30000
Nope. That wasn't it.
So, if #1 costs 3000 more than either #2 or #3, we have
x + y + z = 15000
x = y + 3000
x = z + 3000
3x + 2y + 2z = 30000
No joy there, either.
So, what about the choices?
A: 3*9 + 2*(2+4) = 43 Nope
B: same answer
C: 3*8 + 2*(3.5+3.5) = 38 Nope
D: 3*10 + 2*(4+1) = 40 Nope
E: 8+3+1 ≠ 15
So, where's the typo? I suspect the value increased to $40,000, rather than $30,000, making D the answer.

Math  Hmmm  Steve, Wednesday, March 19, 2014 at 11:23am
No, C is out because 8 ≠ 3.5+3.5+3
D is out because 10 ≠ 1+4+3
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