# Digit Problems

Students learn to solve digit word problems using a system of linear equations, as demonstrated in the following problem. The sum of the digits of a two-digit number is 7. The value of the number is 2 less than 12 times the tens digit. Find the number. The two variables used in this problem are t, the tens digit, and u, the units digit. Since the sum of the digits of the two-digit number is 7, one equation is t + u = 7. Since the value of the number is 2 less than 12 times the tens digit, the other equation is 10t + u = 12t – 2. Note that 10t + u is used to represent "the value of the number". Other problems in this lesson involve "the value of the number with the digits reversed", which can be represented as 10u + t.