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. 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, how much grass does a young sheep consume per day, in pounds?

8 pound of grass  a young sheep consume per day .

Step-by-step 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 .