Answer:
the number could be any of these numbers (111, 128, 145, 162, 179, 196)
Step-by-step explanation:
From the given information, let the number that I'm thinking of to be p
p is > 100
p is < 200
and p = 9 (mod 17)
This implies that 17 ÷ p -9
p - 9 = 17q
here;
q is an integer
p = 9 + 17q
However,
100 < p < 200
= 100 < 9+17q < 200
= 100 - 9 < 17q < 200 -9
= 91 < 17q < 191
Dividing both sides by 17; we have:
= [tex]\dfrac{91}{17}< q < \dfrac{191}{17}[/tex]
= 5.45 < q < 11.24
thus the possible values of q are between 6,7,8,9,10 and 11
The possible values of p can now be:
p = 9 +17(q)
p = 9+17(6), 9+17(7), 9+17(8), 9+17(9), 9+17(10), 9+17(11)
p = 111, 128, 145, 162, 179, 196
Therefore, the number could be any of these numbers (111, 128, 145, 162, 179, 196)
