Question

A farmer has some sheep. The total weight of these sheep is 114 kg.

The farmer buys three more sheep. The mean weight of these three sheep is 26 kg.
The mean weight of all the sheep is 24 kg.
Calculate how many sheep the farmer has after he has bought the three sheep.​

Answer 1

8 sheep total after buying 3 sheep

Explanation:

At the beginning, the farmer had 114 kg of sheep, bu do not know how many.

let x = unknown number of sheep at the beginning.

mean weight = (total weight)/(x + 3) = 24 kg.

mean weight of 3 = 26 kg.

Total weight of the 3 sheep together = 3*26 = 78 kg.

mean weight = ( 114 kg + 78kg) / (x + 3) = 24 kg.

we can solve for x now.

192 / (x + 3 ) = 24

192/24 = x + 3

x + 3 = 8 sheep total after buying

Answer 2

8

Explanation:

The relationship between the total weight, the mean weight, and the number of sheep is ...

mean weight = (total weight)/(number of sheep)

This formula can be rearranged to help us find what we need. For example, ...

number of sheep = (total weight)/(mean weight)

and

total weight = (mean weight)(number of sheep)

__

Using this latter formula, we can find the total weight of the new sheep. It is ...

weight of 3 new sheep = (26 kg)(3) = 78 kg

Then the total weight of all sheep is ...

weight of all sheep = (weight of some sheep) + (weight of 3 new sheep)

= (114 kg) + (78 kg) = 192 kg

Now, we can use the formula for the number of sheep:

number of sheep = (192 kg)/(24 kg) = 8

After buying 3 more sheep, the farmer had 8 sheep.