A library has 6 floors. There are 10 000 more books on the second floor than the first. The number of books on the third floor is the same as the number on the second. There are 10 000 fewer books on the fourth floor than the third and twice as many books on the fifth floor as there are on the fourth. On the sixth floor there are 4 000 fewer books than on the fifth. Coincidentally the number of books on the sixth floor is the same as the number on the first. Altogether, how many thousands of books are there in the library? [1 mark]
Let there be x thousand books on the first floor.
On the second floor there are x + 10 thousand books.
On the third floor there are x + 10 thousand books.
On the fourth floor there are x thousand books.
On the fifth floor there are 2x thousand books.
On the sixth floor there are 2x − 4 thousand books.
Thus we have 2x − 4 = x and so x = 4. The total number of
books, in thousands, is therefore
x + x + 10 + x + 10 + x + 2x + x = 7x + 20= 7 × 4 + 20 = 48.
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Australian Junior Mathematics Olympiad
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1. Download Soal olimpiade Matematika SMP (Australian Junior Mathematics olympiad) 2008-2009
2. Download Soal Olimpiade Matematika SMP tk. Provinsi dan pembahasan
3. Soal Olimpiade Matematika Internasional SMP ( Junior Mathematics Olympiad)