word probs: how many animals of each kind? investments

[AmyTucker]

2. A farm has chickens, turkeys, cows, sheep and dogs for a total of 76 animals. The animals have a total of 280 legs (none of the animals are missing any legs). There are twice as many turkeys as chickens, twice as many cows as sheep, and ten times as many cows as dogs. How many animals of each kind are there?

I know you use these equations, but I don't know how to work it out any further:

Chickens - A
Turkeys - B
Cows - C
Sheep - D
Dogs - E

2A = B
2D = C
10E = C
2A + 2B + 4C + 4D + 4E = 280
A + B + C + D + E = 76

3. An investment club has $900,000 earmarked for investment in stocks. In order to maintain an acceptable overall level of risk, the stocks that the club is considering for investment have been organized into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will give a rate of return of 16 percent per year; medium-risk stocks will give 9 percent per year, and low-risk stocks will give 4 percent per year. The investment in medium-risk stocks must be twice the investment in stocks of the other two categories combined. If the goal is to have an average rate of return of 10 percent per year on the total investment, determine how much the club should invest in each type of stock.

I know you use these equations, but there is more needed and I don't know what they are:

90,000 = .16H + .09M + .04L
M = 2(H + L)

Please help me! Thank you!

 

[tkhunny]

You could try more meaningful names for your variables. That might help you to be less confused.

Maybe:
Chickens - C
Turkeys - T
Cows - W
Sheep - S
Dogs - D


Have you tried H + M + L = 900000? Good call on the variable names!

 

[stapel]

Note: Other post(s) of this exercise have been deleted. Please post only once. Thank you.

Eliz.

 

[Denis]

A farm has chickens, turkeys, cows, sheep and dogs for a total of 76 animals. The animals have a total of 280 legs (none of the animals are missing any legs). There are twice as many turkeys as chickens, twice as many cows as sheep, and ten times as many cows as dogs. How many animals of each kind are there?

Keep the variables as low as possible:
c = chickens; then turkeys = 2c
d = dogs; then cows = 10d and sheep = 5d
So 3c + 16d = 76
and
2(3c) + 4(16d) = 280

Take over.

 

[Denis]

An investment club has $900,000 earmarked for investment in stocks. In order to maintain an acceptable overall level of risk, the stocks that the club is considering for investment have been organized into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will give a rate of return of 16 percent per year; medium-risk stocks will give 9 percent per year, and low-risk stocks will give 4 percent per year. The investment in medium-risk stocks must be twice the investment in stocks of the other two categories combined. If the goal is to have an average rate of return of 10 percent per year on the total investment, determine how much the club should invest in each type of stock.

Same idea.
h = high, w = low; then m = 2(h + w)
h + w + 2(h+w) = 900000
and:
[.16h + .04w + .09(2(h + w))] / 900000 = .10

Take over.