1) If 554 base b is the base b representation of the square of the number whose base b representation is 24 base b then find b.
2) A math textbook with a double-digit number of pages is split into sections. Each section is exactly 12 pages long, with the exception of the epilogue, which is 11 pages long. Every page belongs to a section. Furthermore, on the bottom of each 5th page, a trivia fact is presented on the bottom of the page, starting from the fifth page. If a trivia fact appears on the bottom of the second-to-last page, then how many pages does the textbook have?
3) When a positive integer is expressed in base 7, it is AB base 7 , and when it is expressed in base 5, it is BA base 5. What is the positive integer in decimal?
I don't understand 1) and 2) but I've already answered 3). The answer is 34.
See original post here: https://web2.0calc.com/questions/help-please_35339
I think the answer to the third one is 17 base 10
base 5 would be 32
base 7 would be 23
1) 554 in base b 5*(b^2) + 5(b) + 4
must equal 24b2 = [2(b)+4) ]2
Eqaute the two of them:
5b^2 + 5b + 4 = 4b^2 +16b+16
b^2 -11b-12 = 0
(b-12)(b+1) = 0 b = 12 (throw out the b = -1)
12 sections * x pages + 11 pages must be less than 100 and a multiple of 5 + 1
12(x) + 11 < 100 11 is already a multiple of 5 + 1
so we need 12x to be a multiple of 5 60 will work nicely so x = 5 (the next multiple of 5 would be 120....too big)
12(5) + 11 = 71 pages (assuming 2nd to last page = next to last page)