To find the missing digits \(a\) and \(b\) in the total bill for 99 textbooks represented as \(a482.7b\), we can approach the problem step by step.
First, let's denote the price of each textbook as \( p \). Therefore, the total bill can be expressed as:
\[ 99p = a482.7b \]
To start, we know that \( a482.7b \) must be a multiple of 99 (since it's the total cost of 99 textbooks). Next, let's find the range of \( 99p \).
Since \( 99p \) represents a monetary amount, it must be an integer. Thus, \( a482.7b \) suggests that the last digit \( b \) leads to an integer, meaning \( b \) must be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, and it should make \( 7b \) a digit from 0 to 9 (so \( b \) will be crucial to determine).
- The last digit \( b \) affects the total cost \( 99p \). The last digit of \( 99p \) will depend on the last digit of \( p \). Since \( 99 \) ends with \( 9 \), the last digit of \( 99p \) will be equal to the last digit of \( 10 \) minus the last digit of \( p \).
Now let’s focus on the actual values of \( a \) and \( b \).
- The entire quantity \( a482.7b \) will need to be a multiple of \( 99 \).
Let's analyze with some examples.
To keep checking for plausible values, we can set \( b = 0 \) first and around this we can find suitable values for \( a \).
\[ a482.700 \] This should be divisible by 99. Checking the remainder can be done using modulo operations, but another strategy is calculating directly.
Given that \( 99 \times 5 = 495 \), \( 99 \times 6 = 594\), and so forth. \( 99 \times 10 = 990\) can give certain approximations.
Doing that we get iterative values that may lead us there \( 99(48.27) \approx 4827.0 \).
Through these trials, we can see that the number \( 99 \times 485 \) may conclude a final estimate around \( 45279 \).
Finding exact dividends may swap back to setting values of \( p \) to validate integrity and ensure their timely order.
In summary, the only important values that would help check are around \( a = 4, b = 0\) leading \( 482.700\) which will initially not lead fully.
Conclusively, deliver all integer outputs leading to x = leading integers based on direct calculation thus numerically filled should show from digging through numerous exchanges to consider digits as \( 4827.70\).
Hence the right digits, through pursuit, yield:
\( a = 4, b = 0\) (leading the text through assume yielded tests would initially set these numbers as plausible variables.)
Therefore the missing digits are \(4\) and \(0\).