Question

Of the 45 animals on the farm, there are only pigs and chickens. The animals have a total of 124 legs. How many pigs and how many chickens are on the farm?
A. Write a system of equations to describe the situation. Be sure to define your variables.
b. Solve the system. Show all your work. How many pigs and chickens are on the farm?

Answer 1

Answer:

$on \: this \: farm \: there \: are \to \\ \underline{ \boxed{17 \: pigs }}\: \\ and \\ \underline{ \boxed{28 \:chickens}}$

Step-by-step explanation:

$\\ \underline{ \boxed{solution \: to \: question \: \boxed{ A}}} \\ \\ let \: the \: pigs \: be \to \: p \\ let \: the \: chicks \: be \to \: c \\let \: the \: total \: animals \: be \to \: 45 \\ hence \to \\ p + c = 45.......eq(1) \\ since \: chickens \: have \: two \: legs : \\ while \: pigs \: have \: four \: legs : \\ let \: animals \: with \: 2 \: legs \: be \to \: 2c \\ let \: animals \: with \: 4\: legs \: be \to \: 4p \\ the \: total \: number \: of \: animal \: legs = 124 \\ hence \to \\ 4p + 2c = 124..........eq(2) \\ therefore \: the \: system \: of \: equations \: \\ to \: describe \: the \: situation \: is \to \\ \\ p + c = 45 \\ 4p + 2c = 124 \\ \\ \\ \underline{ \boxed{solution \: to \: question \: \boxed{B }}} \\ \\ \\ we \: could \: apply \: any \: of \: the \: simultanious \\ principles \to \\ here : am \: appling \: the \: elimination \: method \to \\ p + c = 45 \\ 4p + 2c = 124 \\ to \: elimnate \: one \: varaible \: we \: multiply \: by \to \\ (4) \times p + c = 45 \\ (1) \times 4p + 2c = 124 \\ hence \to \\ - \frac{4p + 4c = 180}{4p + 2c = 124} \\next \to \\ 2c = 56 \\ c = \frac{56}{2} \\ \boxed{ c = 28} \\ lets \: work \: for \: p \to \\ p + c = 45 \\ p + 28 = 45 \\ p = 45 - 28 \\ \boxed{p = 17}$