Math  PreCalc (12th Grade)
posted by Shawna on .
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

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? 
I believe combined.

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 
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. 
No, C is out because 8 ≠ 3.5+3.5+3
D is out because 10 ≠ 1+4+3