Pagans

Jano and Michael ate pagans. Jano ate three more than Michael. The product of their counts (numbers) is 180. How many pagans did each of them eat?

Correct answer:

j =  15
m =  12

Step-by-step explanation:

$$\begin{gathered} j\cdot m=180 \\ j=3+m \\ j\cdot (j-3)=180 \\ j\cdot (j-3)=180 \\ {j}^2-3j-180=0 \\ a=1;b=-3;c=-180 \\ D=b^2-4ac=3^2-4\cdot 1\cdot (-180)=729 \\ D>0 \\ {j}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{3\pm \sqrt{729}}{2} \\ {j}_{1,2}=\frac{3\pm 27}{2} \\ {j}_{1,2}=1.5\pm 13.5 \\ {j}_1=15 \\ {j}_2=-12 \\ j=j_1=15 \end{gathered}$$

Our quadratic equation calculator calculates it.

$m=j-3=15-3=12$

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