Question

Forty-five cows and nine horses eat a total of 369 kg of grass in
one day. The farmer also notices that in one day, 4 horses eat 3
kg more grass than 3 cows. How many kilograms of grass does
each kind of animal eat per day?

Answer 1

Answer:

Each Cow eats 7 kg and each Horse each 6 kg per day

Step-by-step explanation:

45C + 9H = 369

4H = 3C + 3

H = 3C/4 +3/4  

45C + 9(3/4C + 3/4) = 369

45C + 27/4C + 27/4 = 369  (Multiply both sides by 4)

45C (4) + 27C + 27(4) = 369(4)

180C +27C = 1476-27

207C=1449

C=1449/207=7  (substitute C=7 back into one of top equations)

4H = 3(7) +3

H = (21+3)/4 = 24/4 = 6

Answer 2

The kilogram of grass eaten by the cow is 7kg and the  kilogram of grass eaten by the horse is 6kg.

The two simultaneous equations that can be derived from the question:

9h + 45c = 369 equation 1

4h = 3c + 3

4h - 3c = 3 equation 2

Where:

c = kg eaten by cows

h = kg eaten by horses

What is the value of h?

In order to determine the value of h, multiply equation 2 by 15

60h - 45c = 45 equation 3

Subtract equation 3 from equation 1

69h = 414

h = 6kg

What is the value of c?

Substitute for c in equation 2

4(6) - 3c = 3

24 - 3c = 3

21 = 3c

c = 7

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552