Question

If a farmer in Kansas purchases 8 pigs for every 1.5 acres of land and has 6 acres of land set aside for pigs, how many pigs will she purchase?

Answer 1

Hint: 8 pigs are purchased for every 1.5 acres of land. So find how many pigs are purchased per acre of land and use it to determine the number of pigs purchased for 6 acres of land.

Complete step-by-step answer:
It is given that the farmer in Kansas purchases 8 pigs for every 1.5 acres of land devoted for raising pigs.
We know that if ‘a’ pigs are purchased for every ‘b’ acres of land, then the number of pigs purchased per acre of land is \[\dfrac{a}{b}\].
Then, if 8 pigs are purchased for every 1.5 acres of land, then, to obtain the number of pigs purchased per acre of land, we just divide 8 by 1.5 to get as follows:
Number of pigs purchased per acre of land = \[\dfrac{8}{{1.5}}............(1)\]
Then, we need to find the number of pigs purchased for 6 acres of land.
We know that to find the number of pigs purchased for a particular acre of land, we need to multiply the number of acres of land with the number of pigs purchased per acre. Hence, from equation (1), we have:
Number of pigs purchased for 6 acres of land = \[6 \times \dfrac{8}{{1.5}}\]
Number of pigs purchased for 6 acres of land = \[4 \times 8\]
Number of pigs purchased for 6 acres of land = \[32\]
Hence, 32 pigs are purchased for 6 acres of land.

Note: We can also directly observe that 6 acres is 4 times 1.5 acres and hence, the number of pigs purchased will be 4 times that of eight. In this way also we get the same answer as 32 pigs.