Single-digit 80674

There are cows, ducks, and geese on the farm. They have a total of 126 legs. Ducks are 3 more than houses. And there are 20 cows. If we count all the animals, we have to divide them by the number three, and we should get a single-digit number.

Correct answer:

a =  13
b =  10
n =  43

Step-by-step explanation:

$$\begin{gathered} k=20 \\ 4k+2a+2b=126 \\ a=3+b \\ 4\cdot 20+2a+2b=126 \\ a=3+b \\ 4\cdot 20+2\cdot a+2\cdot b=126 \\ a=3+b \\ 2a+2b=46 \\ a-b=3 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+2b=46 \\ -2b=-20 \\ b=\frac{-20}{-2}=10 \\ a=\frac{46-2b}{2}=\frac{46-2\cdot 10}{2}=13 \\ a=13 \\ b=10 \end{gathered}$$

$$\begin{gathered} n=k+a+b=20+13+10=43 \\ \text{ Verifying Solution: } \\ x=n/3=43/3=\frac{43}{3}=14\frac{1}{3}\doteq 14.3333 \end{gathered}$$

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