Answer:
(a) 11608
(b) 4469 (base 12)
Explanation:
The number system we use in daily life has base 10 (decimal). There are many others bases used and conversion from one base to another is done on specific rules.
Each part is calculated and explained in the image attached.
The beverage cans  value is "11608 cans", and representation in base 12 is "[tex]\bold{4469_{12}}[/tex]"
For question a)
[tex]\to 6\ \text{great gross} + 8 \ \text{gross}+ 7 \text{dozen} +4\\\\ \to 6 \times 12^3 + 8 \times 12^2 + 7\times 12 + 4 \\\\\to 6 \times 1728 + 8 \times 144 + 7\times 12 + 4 \\\\\to 10368+1152+84+4\\\\\to 11608\ \text{cans}\\\\[/tex]
For question b)
    Quotients   Â
[tex]12 \ \ \ \ \ \ 7569 \ \ \ \ \ \ Remainder\\\\12 \ \ \ \ \ \ 630 \ \ \ \ \ \ 9\\\\12 \ \ \ \ \ \ 52 \ \ \ \ \ \ 6\\\\12 \ \ \ \ \ \ 4 \ \ \ \ \ \ 4\\\\[/tex]
     [tex]\ \ \ \ \ \ 0 \ \ \ \ \ \ 4\\\\[/tex]
writing the remainders from bottom to top:
[tex]\to (7569)_{10} = (4469)_{12}[/tex]
Therefore, the final answer is "11608 cans and [tex]\bold{4469_{12}}[/tex]".
Find out more information about the math system here:
brainly.com/question/13382169
