If the 10-digit number 96530y15x8 is divisible by 72, then what is the value of (3x−7y) for the maximum value of x?

A number is divisible by 72 if it is divisible by both 8 and 9.
1. Divisibility by 8:
The last three digits 5x8 must be divisible by 8.
Let's check values of x from 9 downwards to maximize x:

If x=9: 598÷8=74.75 (No)

If x=8: 588÷8=73.5 (No)

If x=7: 578÷8=72.25 (No)

If x=6: 568÷8=71 (Yes)

Thus, the maximum value of x=6.

2. Divisibility by 9:
The sum of all digits must be divisible by 9.

Sum=9+6+5+3+0+y+1+5+x+8
Sum=37+x+y
Substitute x=6:

Sum=37+6+y=43+y
For 43+y to be divisible by 9, y must be 2 (since 45 is divisible by 9).
So, y=2.

3. Evaluate (3x−7y):

3x−7y=3(6)−7(2)=18−14=4