Question

if you have $100 and you have to buy 100 animals cows cost $10 pigs cost $3 and chickens cost $0.50

...find no.of animals​

Answer 1

Answer:

Let x = no. of cows

Let y = no. of pigs

Let z = no. of chicks

:

The no. of animal equation:

x + y + z = 100

:

The cost of animals equation

10x + 3y + .5z = 100

:

Multiply above equation by 2 and subtract the 1st equation:

20x + 6y + 1z = 200

x + y + z = 100

----------------------subtracting eliminates z

19x + 5y = 100

:

We know that x and y are integers; 19x and 5y have to be multiples of 5:

That leaves the only value we can have for x is 5

:

5 cows

 

:

19(5) + 5y = 100

95 + 5y = 100

5y = 100-95

5y = 5

y = one lonesome pig

:

5 cows and 1 pig would leave us with 94 chickens

:

Check our solutions in the cost equation

10(5) + 3(1) + .5(94) =  

50.00 + 3.00 = 47.00 = $100