Question

. On a farm the number of cows and the number of sheep are in the ratio 6:5
the number of sheep and the number of pigs are in the ratio 2:1
The total number of cows, sheep and pigs on the farm is 189
How many sheep are there on the farm?
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Answer 1

Answer:

There were 70 sheeps in the farm.

Step-by-step explanation:

Let the number of cows be 6x and number of sheeps be 5x

But given,

So,

Let the number of sheeps be 2y and number of pigs be y.

Now, if we notice the number of sheeps,

They have to be equal no matter the variables.

So,

5x = 2y

x = (2/5)y

Then,

The number of cows will be 6x = 6 × (2/5)y

= (12/5)y

The number of sheeps will be 5x = 5 × (2/5)y

= 2y

Hence,

They are in the ratio,

(12/5)y : 2y : y

Again, we are given that,

Total number of cows, sheeps and pigs = 189

So,

We can say that,

(12/5)y + 2y + y = 189

Then, solving for y

(12/5)y + 2y + y = 189

(12/5)y + 3y = 189

(12/5)y + (15/5)y = 189

(12y + 15y)/5 = 189

27y/5 = 189

27y = 5 × 189

27y = 945

y = 945/27

y = 35

Now,

We know that,

Number of sheeps = 2y

= 2 × 35

= 70 sheeps

Hence,

There were 70 sheeps in the farm.

Hope it helped and believing you understood it. All the best.