What are the possible values for the first of the two numbers? ?

Question

The sum of two numbers is greater than or equal to 26 . The second number is 8 more than the first.

Answer 1

Let

X = smaller number or the first number

Y = second number

<<  sum of two numbers is greater than or equal to 26 . >>

X + Y >= 26

<< The second number is 8 more than the first. >>

Y = X + 8

Substituting Y = X + 8 in the inequality,

X + (X + 8) >= 26

2X + 8 >= 26

2X >= 18

X >= 9

CHECK:

If the first number is 9, then the second number will have to be 17 (9 + 8).

9 + 17 >= 26

Hope this helps.

Answer 2

Let A and B be the two numbers.  Then A+B >= 26.  Also, B = A+8.  Plug that into the first inequality to get A+(A+8) >= 26.  This means

2A + 8 >= 26

2A >= 18

A >= 9