Library book increase

The number of books in the city library increased by 0.2% in 2008 and 0.6% in 2009. At the same time, the total number of books remained less than 300,000. How many books were added to the city library in 2009?

Final Answer:

x =  1503

Step-by-step explanation:

q1​=100%+0.2%=1+1000.2​=1.002 q2​=100%+0.6%=1+1000.6​=1.006  q=q1​⋅ q2​=1.002⋅ 1.006≐1.008 k1​ = n/q2​ n<300000  a ⋅  q1​ = x x ⋅  q2​ < 300000  1002 ⋅  a   = 1000 ⋅  x 1006 ⋅  x   < 1000⋅  300000  300000 = 25 × 3 × 55 501 = 1⋅ 501 503 = 1⋅ 503 500 = 22 × 53  501 ⋅  a = 500⋅ x 503 ⋅  x < 500⋅ 300000 503 ⋅  501 ⋅  a < 500 ⋅  500⋅ 300000 252003 ⋅ a < 250000 ⋅  300000 252003 ⋅ 250000 < 250000 ⋅  300000 252003 <  300000  a=500⋅ 500=250000 b=q1​⋅ a=1.002⋅ 250000=250500 c=q2​⋅ b=1.006⋅ 250500=252003  x=c−b=252003−250500=1503

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