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Sagot :
If Dionte creates a list, it will be (3*n, 9*n) where "n" is the number of books, then, we have the pattern:
[tex](3n,9n)\quad n\in\mathbb{N}[/tex]But how do discover which one should be on the list? See that the first coordinate is divisible by 3, if we divided it by 3 we have just "n", if we do divide the second coordinate by 9 we have just "n" as well. Then we have to divide by three the first coordinate and by 9 the second one, after that they must be the same! if they are the same it's correct.
a)
[tex](6,27)_{}[/tex]Let's do our logic, divide by 3 and the other by 9
[tex](\frac{6}{3},\frac{27}{9})=(2,3)[/tex]As we can see it's different, so it couldn't be on Dionte's list.
b)
Doing the same thing
[tex](\frac{12}{3},\frac{36}{9})=(4,4)[/tex]The result is (4,4), two equal numbers, then it could be on Dionte's list.
c)
[tex](\frac{15}{3},\frac{45}{9})=(5,5)[/tex]The result is (5,5), two equal numbers, then it could be on Dionte's list.
d)
[tex](\frac{18}{3},\frac{54}{9})=(6,6)[/tex]The result is (6,6), two equal numbers, then it could be on Dionte's list.
e)
[tex](\frac{24}{3},\frac{81}{9})=(8,9)[/tex]Here we have a different result again, then it couldn't be on Dionte's list.
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