Question

Farmer frank owns a piece of grassland. The grass grows at a constant rate and each cow eats at a constant rate. 12 cows can eat 10 acres of grass in 28 days. 21 cows can eat 30 acres of grass in 63 days. How many cows can eat 72 acres of grass in 126 days?

Answer 1

Answer: There are 36 cows that can eaten 72 acres of grass in 126 days.

Step-by-step explanation:

Let x be the amount of grass in an acre initially.

Let y be the amount of grass grown in an acre per day.

Since we have given that

12 cows can eat 10 acres of grass in 28 days

12×28  = 10x + 10×28 y

336 = 10x + 280 y----------------------------(1)

Similarly,

21 cows can eat 30 acres of grass in 63 days.

21×63  = 30x + 30×63 y

1323 = 30x +1890 y ---------------------------(2)

So, by graphing method, we get the value of x and y

$x=\dfrac{126}{5},\ y=\dfrac{3}{10}$

So, we have,  72 acres of grass in 126 days, we need to find the number of cows.

So, it becomes,

c×126 = 72x + 72×126 y

$126c=72\times \dfrac{126}{5}+72\times 126\times \dfrac{3}{10}\\\\126x=4536\\\\x=\dfrac{4536}{126}\\\\x=36$

Hence, there are 36 cows that can eaten 72 acres of grass in 126 days.