Help I have a question, not easy for me but will be easy for you?

Question

This is for a 7th grade girl I babysat we never learn this.

Ok,

On the paper it says

I have 100 bucks and I have to have 100 animals no more or less same with money

Ok I have to use at least all these animals at least one

Pigs: 3 buck each

Cows: 10 buck each

Sheep 50cent each

I cant figure it out I have to spend exactly 100 and have 100 animals

help?

please show all work

Answer 1

Since cows are $10 each, the pigs and sheep have to make a total which is a multiple of 10 (10, 20, 30, etc.)

e.g. with 9 cows, we could have a pig($3) and 14 sheep ($7), or 2 pigs and 8 sheep, or 3 pigs and 2 sheep. But none of those are enough animals.

With 1 cow, we could have a pig and 174 sheep, but that's too many animals.  We could go on like that using guess and check, but let's try some equations:

Say there are x pigs, y cows and z sheep.

Then x + y + z = 100

and 3x + 10y + 0.5z = 100

The second equation is equivalent to

6x + 20y + z = 200

and if we subtract the first one from that we get

5x + 19y = 100

Therefore 19y = 100 - 5x

The right-hand side has 5 as a factor, and it must be less than 100 (x is positive).

Therefore.y = 5 and 19y = 95

hence 100 - 5x = 95

and so 5x = 5

x = 1

Since x + y + z = 100, we now have

1 + 5 + z = 100

Therefore z = 94

94 sheep are worth $47

1 pig .................... $3

5 cows ................. $50