Readers

Readers borrowed 220 books from the library during the first three days. On the second day, readers borrowed half as many books as on the first day and, at the same time, 20 fewer books than on the third day. Depending on the quantity x, express the number of books readers borrowed the next day. Depending on the quantity x, express the number of books readers borrowed on the third day. Calculate how many books readers borrowed on the first day.

Final Answer:

x =  75
a =  50
c =  95

Step-by-step explanation:

$$\begin{gathered} 220=a+x+c \\ x=a+a/2 \\ c=x+20 \\ x=3/2\cdot a \\ a=2/3\cdot x \\ 220=(2/3\cdot x)+x+(x+20) \\ 8x=600 \\ x=\frac{600}{8}=75 \\ x=75 \end{gathered}$$

$a=\frac{2}{3}\cdot x=\frac{2}{3}\cdot 75=\frac{2\cdot 75}{3}=\frac{150}{3}=50$

$$\begin{gathered} c=x+20=75+20=95 \\ \text{ Verifying Solution: } \\ s=a+x+c=50+75+95=220 \end{gathered}$$

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