Let's write the two-digit number as AB, where A is the tens digit, and B the units. We have:
A = 5 + B (the tens digit of a two-digit number is five more than the units digit)
The number AB can be written as:
10A + B
So, since it equals the sum of its digits multiplied by 8, we have:
10A + B = 8(A + B)
10A + B = 8A + 8B
10A + B - 8A = 8A + 8B - 8A
2A + B = 8B
2A + B - B = 8B - B
2A = 7B
Thus, to find that number, we need to solve the following system of equations:
A = 5 + B
2A = 7B
We can replace A in the second equation with 5 + B, to obtain:
2(5 + B) = 7B
10 + 2B = 7B
10 + 2B - 2B = 7B - 2B
10 = 5B
10/5 = 5B/5
2 = B
B = 2
Now, A is given by:
A = 5 + 2 = 7
Therefore, the number is 72.