2006-11-20 06:14:12 · 4 answers · asked by MB 3 in Science & Mathematics ➔ Mathematics
There are several possible answers:
329
455
581
707
833
Details:
329 is odd, 329/7 = 47, 3 + 2 + 9 = 14
455 is odd, 455/7 = 65, 4 + 5 + 5 = 14
581 is odd, 581/7 = 83, 5 + 8 + 1 = 14
707 is odd, 707/7 = 101, 7 + 0 + 7 = 14
833 is odd, 833/7 = 119, 8 + 3 + 3 = 14
2006-11-20 06:20:26 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
So, number ABC.
We know that 100A+10B+C=7n, that C is odd, and that A+B+C=14.
Subtracting the two equations:
99A + 9B = 7n-14
9A+B = (7n-14)/9
This means 7n-14 is a multiple of 9.
7n-14 = 0 modulo 9
7n = 14 mod 9
n = 2 mod 9, or n=9i+2 for some i. Also i must be odd for n to be odd for 7n to be odd.
Let's try some possibilities:
i=1, n=11, ABC=077 - not a 3-digit number
i=3, n=29, ABC=203 - must add to 14
i=5, n=47, ABC=329 - Got it!
i=7, n=65, ABC=455 - Works too!
i=9, n=83, ABC=581 - Yessss!
i=11, n=101, ABC=707 - BOEINGGGG!
i=13, n=119, ABC=833 - Wohooo!
n=15, n=137, ABC=959 - no, adds up to 23.
So we have 5 solutions: 329, 455, 581, 707 and 833.
2006-11-20 14:27:26 · answer #2 · answered by Anonymous · 0⤊ 0⤋
329
2006-11-20 14:18:37 · answer #3 · answered by frodobaggins115 4 · 0⤊ 0⤋
the number is 581
2006-11-20 14:27:50 · answer #4 · answered by blueskies 7 · 0⤊ 0⤋