Question

there are 17 animals in a field.some are goats and some are pigs. there are 92 legs in all. How many of each animal are in the field. using the process of elimination.​

Answer 1

By using the process of elimination with the fact that there are 92 legs and 17 animals, we determined that there are 11 goats and 6 pigs in the field. A careful step-by-step calculation helped us solve this problem.

Step-by-step explanation:

The student is asking how many pigs and goats are in a field if there are 17 animals and 92 legs in total. We can solve this problem using a system of equations or by process of elimination.

Step-by-Step Solution

1. Let's assume all animals are goats with 4 legs. That would be 17 goats × 4 legs/goat = 68 legs. But there are 92 legs, so there must be some pigs (which have 4 legs more than goats).
2. Since every pig will add 4 more legs than a goat, we can calculate how many extra legs there are that could come from pigs. 92 total legs - 68 legs if all were goats = 24 extra legs. These extra legs must be from pigs.
3. Since pigs have 4 legs, we divide the 24 extra legs by 4 to find the number of pigs: 24 extra legs ÷ 4 legs/pig = 6 pigs.
4. Now we know there are 6 pigs, and since there are 17 animals in total, we can find the number of goats. 17 total animals - 6 pigs = 11 goats.
5. Finally, we multiply the number of each animal by their respective number of legs to ensure that the total adds up to 92. (11 goats × 4 legs) + (6 pigs × 4 legs) = 44 + 24 = 68 + 24 = 92 legs.
6. So, the field has 11 goats and 6 pigs which add up to a total of 92 legs, confirming the reasonableness of our answer process of elimination.

Therefore, there are 11 goats and 6 pigs in the field.