linear equations

Question

The sum of two integers is 23. The larger is 13 less than three times the smaller. Find the two integers.

Answer 1

If we let the smaller number be represented by the variable, x, then we can write the expression 3x - 13 to represent the larger integer.

Since the sum of the two integers is 23, we can write the following equation:

x + 3x - 13 = 23

Now combine like terms and use inverse operations to solve for x (or the smaller number):

x + 3x - 13 = 23

4x - 13 = 23

4x - 13 + 13 = 23 + 13

4x = 36

4x/4 = 35/4

x = 9

The smaller integer is 9

The larger number will be 3x - 13 OR 3*9 -13 = 27 -13 = 14

The larger integer is 14.

NOTE that the sum of 14 and 9 is 23.