Scratches

The ticket seller sold 1,280 scratch cards in three days. He sold 90 tickets less on the second day than on the first day. He sold 1.5 times more tickets on the third day than on the second day. How many tickets did he sell on the third day?

Final Answer:

c =  510

Step-by-step explanation:

$$\begin{gathered} a+b+c=1280 \\ b=a-90 \\ c=1.5b \\ c=1.5\cdot b \\ a+b+c=1280 \\ a-b=90 \\ 1.5b-c=0 \\ Row2-Row1\to Row2 \\ -2b-c=-1190 \\ Row3-\frac{1.5}{-2}\cdot Row2\to Row3 \\ -1.75c=-892.5 \\ c=\frac{-892.5}{-1.75}=510 \\ b=\frac{-1190+c}{-2}=\frac{-1190+510}{-2}=340 \\ a=1280-b-c=1280-340-510=430 \\ a=430 \\ b=340 \\ c=510 \end{gathered}$$

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