Cake ratio

On the tray, they had apricot and plum cakes in a ratio of 3:2. After eating three apricot pies, the chance of taking out a plum and apricot was the same. How many cakes were there together on the tray at the beginning?

Final Answer:

x =  15

Step-by-step explanation:

$$\begin{gathered} a:b=3:2 \\ 2a=3b \\ a-3=b \\ 2\cdot a=3\cdot b \\ 2a-3b=0 \\ a-b=3 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 0.5b=3 \\ b=\frac{3}{0.5}=6 \\ a=\frac{0+3b}{2}=\frac{0+3\cdot 6}{2}=9 \\ a=9 \\ b=6 \\ x=a+b=9+6=15 \end{gathered}$$

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