Gnocchi 3

Mom cooks gnocchi every day. Poppy seeds one day, walnuts the next day, cottage cheese the third day, and all over again. Every day, I eat 3 gnocchi from poppy seeds, 3 from walnut gnocchi, and 2 gnocchi from cottage cheese. I have eaten 46 dumplings so far. How many poppy seeds and how many cottage cheese gnocchi did I eat?

Correct answer:

m =  8
t =  14
o =  24

Step-by-step explanation:

$$\begin{gathered} a=46/(1+3+2)=\frac{23}{3}=7\frac{2}{3}\doteq 7.6667 \\ b=\lfloor a\rfloor =\lfloor 7.6667\rfloor =7 \\ c=46-b\cdot (1+3+2)=46-7\cdot (1+3+2)=4 \\ m=1+b\cdot 1=1+7\cdot 1=8 \end{gathered}$$

$t=b\cdot 2=7\cdot 2=14$

$o=3+b\cdot 3=3+7\cdot 3=24$

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