Question

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is th

integer, which system of inequalities could represent the values of a and b?

Answer 1

`a + b \geq 30`

`b - a \geq 10`

Explanation:

Given

The sum of the two positive integer a and b is at least 30, this means the sum of the two positive integer is 30 or greater than 30, so we write the inequalities as below.

`a + b \geq 30`

The difference of the two integers is at least 10, if b is the greater integer then we subtract integer a from integer b, so we write the inequality as below.

`b - a \geq 10`

Therefore, the following system of inequalities could represent the values of two positive integers a and b.

`a + b \geq 30`

`b - a \geq 10`