The ratio of the units digit to the tens digit of a two-digit number is one-half. The tens digit is 2 more than the units digit. Find the number.

Number : 42

Step-by-step explanation:

This number will be a two - digit number, and hence we can say that it is yz. The ratio of the units digit to the tens digit is given by 1 / 2, so z / y = 1 / 2.

In addition the tens digit is 2 more than the units digit, so y = z + 2. We therefore have the following system of equations,

y = z + 2,

z / y = 1 / 2

Substituting the first equation into the second we receive z / z + 2 = 1 / 2. Using this we can solve for z.

z / z + 2 = 1 / 2 ( Cross - Multiply )

z + 2 = 2z, z = 2

And knowing z we can solve for y. y = z + 2 = 2 + 2 = 4. Therefore our number is 42.