The ratio of the units digit to the tens digit of a two-digit number is one-half. The tens digit is two more than the units digit. Find the number.

The number is 42.

Let xy be the number. x is the tens digit, y is the units digit. The ratio of the units digit to the tens digit, y/x, is 1/2. This gives us the proportion

y/x = 1/2

The tens digit is 2 more than the units digit; x = y+2; substituting in our proportion we have

y / (y+2) = 1/2

Cross multiply:

y*2 = (y+2) * 1

2y = y+2

Subtract y from each side:

2y - y = y+2-y

y = 2

x = y+2

x = 2+2

x = 4

xy = 42