Cheese consumption

I have some cheese. I used 2/5 of the total amount of cheese yesterday. Today, I used 2/5 of the remaining cheese from yesterday.
If 900 g of cheese remains at the end of today, how many grams of cheese did I have initially?

Final Answer:

x =  2500 g

Step-by-step explanation:

$$\begin{gathered} r=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6 \\ x\cdot r\cdot r=900 \\ x\cdot 0.6\cdot 0.6=900 \\ 0.36x=900 \\ x=\frac{900}{0.36}=2500=2500\text{g} \\ x=2500 \\ \text{ Verifying Solution: } \\ a=r\cdot x=0.6\cdot 2500=1500\text{g} \\ b=r\cdot a=0.6\cdot 1500=900\text{g} \end{gathered}$$

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