Final answer:
The missing digit y in the ISBN-10 codeword 1234567y3X is 7. This was found by applying the ISBN-10's check digit calculation formula and checking that the sum is divisible by 11.
Step-by-step explanation:
The student is trying to find the missing digit y in an ISBN-10 code. The ISBN-10 code provided is 1234567y3X, where X represents the check digit, which is 10 in the ISBN system. To find the missing digit y, we can use the ISBN-10's check digit formula:
- Take each of the first nine digits of the ISBN, multiply each by its (integer) position in the number, and add all these products.
- Add the result to 10 times the check digit (X in this case).
- If the result is divisible by 11, then the ISBN is valid.
To solve for y, we can set up the equation based on the ISBN formula:
1×1 + 2×2 + 3×3 + 4×4 + 5×5 + 6×6 + 7×7 + y×8 + 3×9 + 10×10 (since X is 10) = a multiple of 11.
We know the sum of the first eight products and the last term (100 for X) is 202. Now we add 27 (for the digit 3 at the ninth position) and find that we have 229 + 8y. Since this must be a multiple of 11, we can use trial and error to find the value of y that satisfies the equation:
229 + 8y = 11n, where n is a whole number.
By trying different values of y (from 0 to 9, as it must be a single digit), we find that when y = 7, the total is 229 + 8*7 = 285, which is divisible by 11 (11*26 = 286). Therefore, the missing digit y is 7.