Question

A farmhouse shelters 23 animals consisting of pigs and ducks. Altogether there are 80 legs. How many of each animal are there?

Answer 1

Using a system of equations, we calculate there are 17 pigs and 6 ducks in the farmhouse, based on the total number of animals and total number of legs.

Step-by-step explanation:

The student's question involves discovering how many pigs and ducks are in a farmhouse when given the total number of animals and the total number of legs. We can calculate the numbers through a system of equations that considers that pigs have 4 legs and ducks have 2 legs. Let's denote the number of pigs as p and the number of ducks as d.

From the given information, we can establish two equations:

1. p + d = 23 (Total number of animals)
2. 4p + 2d = 80 (Total number of legs)

To solve for p and d, we can multiply the first equation by 2 to align the coefficient of d in both equations, which gives us a new equation: 2p + 2d = 46. By subtracting this new equation from the second equation, we eliminate d and are left with 2p = 34, giving us p = 17. Now, substituting p back into the first equation, we find that d = 23 - 17, so d = 6. Thus, there are 17 pigs and 6 ducks.