math question

[Steve19]

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a friend told me that he got this question on his DAT last year ..
A farmer who has $100.00 and with the hundered dollars he has to buy 100 animals. Listed below are the cost of the animals. Remember only $100.00 and he has to buy 100 animals

Costs

Cows: $10.00
Pigs: $3.00
Chickens: $0.50

ok..how do you solve this kind of problems , and what the answer could be??

 

[wigglytooth]

a friend told me that he got this question on his DAT last year ..
A farmer who has $100.00 and with the hundered dollars he has to buy 100 animals. Listed below are the cost of the animals. Remember only $100.00 and he has to buy 100 animals

Costs

Cows: $10.00
Pigs: $3.00
Chickens: $0.50

ok..how do you solve this kind of problems , and what the answer could be??

I feel like there should be one more constraint on this problem, but I'm not thinking it fully through. All I know is that you can get at least 2 equations from the information given:

1) 10x + 3y + 0.5z = 100 (cost/animal times # of particular animal = what you're going to pay per animal; add up what you're going to pay per animal in total, and you get 100)
2) x + y + z = 100 (you can only get 100 animals in total)

Where x = #cows, y = #pigs, z = #chickens

There's definately another equation that I'm missing, but then you just combine all of the equations to cancel out variables to get the value of one variable. Once you get that, you plug it in to any of your equations and get the others.

 

[issa]

this question is similar to the "how many $5 and $10 bills" question in topscore. if you understand the concept then it will be easier for you to answer any question like these.

 

[Steve19]

ok..i got it ..but without using any equations....
94 chickens
1 pig
5 cows

 

[Rook]

ok..i got it ..but without using any equations....
94 chickens
1 pig
5 cows

10X +3Y +0.5(100 - x - y)= 100

Where X = Cows, and Y = Pigs
(100 - x - y) = Number of Chickens

Simplify:
9.5X + 2.5Y = 50
Simplify Again by Multiplying the equation by 2

19X + 5Y = 100

Ok, Now you have to start using your brain.
We know that X has to be a multiple of 5 in order to add up with Y to give a zero in the 'ones' place right?
10 would be too big, but 5 is just right.
19(5) + 5Y = 100
5Y = 5
Y = 1

5 Cows, 1 Pig, 94 Chickens.
If this explanation does not work for you:
I would back solve this question. Take the answer choices and look for one that works! Best of luck, hope this helps.

 

[Gasedo]

10X +3Y +0.5(100 - x - y)= 100

Where X = Cows, and Y = Pigs
(100 - x - y) = Number of Chickens

Simplify:
9.5X + 2.5Y = 50
Simplify Again by Multiplying the equation by 2

19X + 5Y = 100

Ok, Now you have to start using your brain.
We know that X has to be a multiple of 5 in order to add up with Y to give a zero in the 'ones' place right?
10 would be too big, but 5 is just right.
19(5) + 5Y = 100
5Y = 5
Y = 1

5 Cows, 1 Pig, 94 Chickens.
If this explanation does not work for you:
I would back solve this question. Take the answer choices and look for one that works! Best of luck, hope this helps.

Good explanation Rook. 👍

 

[wigglytooth]

Good explanation Rook. 👍

Yeah, a lot better than my half-assed job 😛 I knew I was missing something.