Baking cakes

Anička and Ema baked cakes together. Ema baked one third more cakes than Anička. Anička kept one third of the cakes for herself, Ema kept half of the cakes she baked. The remaining 12 cakes they gave to their parents.
1) Determine how many cakes Anička and Ema baked in total.
2) Determine how many cakes Anička kept.
3) Determine with precision to one decimal place what % of all cakes Ema baked.

Final Answer:

n =  21
n =  3
p =  57.1 %

Step-by-step explanation:

$$\begin{gathered} e=a+a/3 \\ a+e-a/3-e/2=12 \\ 4a-3e=0 \\ 4a+3e=72 \\ Row2-Row1\to Row2 \\ 6e=72 \\ e=\frac{72}{6}=12 \\ a=\frac{0+3e}{4}=\frac{0+3\cdot 12}{4}=9 \\ a=9 \\ e=12 \\ n=a+e=9+12=21 \end{gathered}$$

$n=b=a/3=9/3=3$

$p=100\cdot \frac{e}{n}=100\cdot \frac{12}{21}=\frac{100\cdot 12}{21}=\frac{1200}{21}=\frac{400}{7}\%=57.1\%$

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