math word probem assistance needed

[lwarner]

:?: The Question: How many animals must Marin buy of each kind of animal?

Marin wants to buy new chickens, pigs, and horse. A new chicken costs 50 cents, a pig is three dollars, and a horse is 10 dollars. Marin has 100 dollars with which she wants to buy exactly 100 animals, but in such a way that she has at least one of each kind of animal.

here's some of my work so far:

A (.5 cents) + B (3.00 dollars) + C (10.00 dollars) = 100 dollars

A + B + C = 100

2A + 3B = 1C

I'm in pre-algebra and we have not covered this type of problem. It's been a long time since my parents had this kind of math. I would appreciate some help.

Thank you

 

[stapel]

Archived solution.

 

[Denis]

2A + 3B = 1C is not correct: how did you ever get that?

> A (.5 cents) + B (3.00 dollars) + C (10.00 dollars) = 100 dollars

That's correct; write it this way: A/2 + 3B + 10C = 100;
since you're buying Chickens, Pigs and Horses, use C,P,H:
C/2 + 3P + 10H = 100 ; multiply by 2 to get rid of fraction:
C + 6P + 20H = 200 [1]

And we also have:
C + P + H = 100
C = 100 - P - H [2]

Substitute [2] in [1]
How does this simplify?

The result cannot be completely solved with algebra;
you now need trial and error.