Help Needed: buying 100 animals for $1000 exactly

HI all, I am taking a college class at the community college and I have no clue how to figure this out. If you can help I would be very thankful.

The Question Is The Following:

You have to spend $1,000.00

You have to buy 100 animals

Cow costs $50.00 each

Sheep costs $10.00 each

Rabbit costs .50cents each

I am desparate for any help you can provide me. This is not a test question or anything like that but I need to know how to perform these types of problems.

Much Appreciated,
Laura

Re: Help Needed - I am Lost

Laura62 said:

HI all,

I am taking a college class at the community college and I have no clue how to figure this out. If you can help I would be very thankful.

The Question Is The Following:

You have to spend $1,000.00

You have to buy 100 animals

Cow costs $50.00 each

Sheep costs $10.00 each

Rabbit costs .50cents each


I am desparate for any help you can provide me. This is not a test question or anything like that but I need to know how to perform these types of problems.

Much Appreciated,

Laura

Click to expand...

Your problem does not restrict you to buy at least one of each kind.

In that case, read the "costs" carefully - you have an easy answer.

Otherwise - you'll have to find the answer by trial and error.

Re: Help Needed - I am Lost

You have to spend $1,000.00
You have to buy 100 animals
Cow costs $50.00 each
Sheep costs $10.00 each
Rabbit costs .50cents each

Click to expand...

Assuming at least 1 of each is purchased:
Let c, s and r be the respective quantities of cows, sheep and rabbits.

Then
1--c + s + r = 100
2--50c + 10s + .5r = 1000 or 100c + 20s + r = 2000
3--Subtracting (1) from (2) yields 99c + 19s = 1900
4--Dividing through by the lowest coefficient yields
...5c + 4c/19 + s = 100

...and so forth. What can you do with this?

Re: Help Needed - I am Lost

I'm sorry I did not make that clear. You have to buy at least one of each animal.

Best Regards,

Laura

Re: Help Needed - I am Lost

The Question Is The Following:
You have to spend $1,000.00
You have to buy 100 animals
Cow costs $50.00 each
Sheep costs $10.00 each
Rabbit costs .50cents each

Since you have 100 animals: C + S + R = 100 [1]
Since you're spending $1000: 50C + 10S + .5R = 1000; multiply by 2 to get rid of decimal:
100C + 20S + R = 2000 [2]

from [1]: R = 100 - C - S ; substitute in [2]:
100C + 20S + 100 - C - S = 2000
99C + 19S = 1900

Now you get C and S by trial and error; easy to see that C is lesser than 20, right?