Base number is the number of digits which have a system of counting to represent the numbers. The least possible value of a+b written in base 10 is 16.
Given information-
The base of both represent the same number. Thus,
[tex]4a+7=7b+4[/tex]
Base number
Base number is the number of digits which have a system of counting to represent the numbers.
Solving it for b,
[tex]\begin{aligned}\\
7b&=4a+7-4\\
b&=\dfrac{4a+3}{7} \\
\end[/tex]
The value of 47 with base is a equivalent to 0. Therefore,
[tex]4a+7\overline =0 \\
[/tex]
Therefore the value of the a is,
[tex]4a\overline = 4\\
a\overline =1[/tex]
As the value of a is 1 with mod 7. Thus the smallest possible value of x can be 8.
As the value of a is 8 and the highest base value is 16. Thus a+b can only be less than or equal to 16.
If b has to written in base 10, thus the value of b must be less than 9. Hence the value of b is 8 which satisfy both the conditions. Thus,
[tex]a+b=8+8=16[/tex]
Therefore the least possible value of a+b written in base 10 is 16.
Learn more about the base number here;
https://brainly.com/question/13436915
