Answer:
8 pound of grass a young sheep consume per day .
Explanation:
As given
On a farm, the ratio of the number of old sheep to young sheep to little sheep is 3:13:4.
There are 600 sheep in total.
Let us assume that x be the scalar multiple of the old sheep ,young sheep and little sheep .
Thus
Number of old sheep = 3x
Number of young sheep = 13x
Number of little sheep = 4x
Equations becomes
3x + 13x + 4x = 600
20x = 600
x = 30
Number of old sheep = 3x
= 3 × 30
= 90
Number of young sheep = 13x
= 13 × 30
= 390
Number of little sheep = 4x
= 4 × 30
= 120
As given
Each old sheep consumes 4.5 pounds of grass per day and each little one consumes 2 pounds of grass each day.
If the sheep on the farm, altogether, eat 3765 pounds of grass each day .
Let us assume that the pound of grass consumes by young sheep per day be u .
Equation becomes
Total pounds of grass consumes by sheeps = Number of old sheeps × Pound of grass consumes by one old sheep each day + Number of young sheeps × Pound of grass consumes by one young sheep each day + Number of little sheeps × pound of grass consumes by one little sheep each day .
Putting all the values in the above
3765 = 90 × 4.5+ 390× u + 120 × 2
3765 = 405 + 390u + 240
3765 - 645 = 390u
3120 = 390u
u = 8 pound
Therefore 8 pound of grass a young sheep consume per day .