One of the digits of a two digit number is 6, whose sum is half of their
product, and whose product is half of the reverse order number. What is
the number?
Let t = the tens digit
Let u = the ones or units digit.
One of the digits of a two digit number is 6.
We aren't told which it is so we have to try both possibilities.
Case 1: u = 6
whose sum is half of their product
t + 6 = ·6t
t + 6 = 3t
6 = 2t
3 = t
So the number is 36
and whose product is half of the reverse order number
The product is 3*6 = 18 but 18 is not half of the reverse 63.
So Case 1 is eliminated, so it's not 36.
Case 2: t = 6
whose sum is half of their product
6 + u = ·6u
12 + 2u = 6u
12 = 4u
3 = u
So the number is 63
and whose product of the half of the reverse order number
The product is 6*3 = 18 and 18 is indeed half of the reverse 36.
So that's it. The number is 63.
Edwin