We will first define variables
Let Mike be M and Beth be B.
First inequality is 25M + 15B ≥ 1975 an the second is B≤ 4M
When we replace B in the first inequality we get
25M + 15*4M ≥ 1975 => 25M + 60M ≥ 1975 => 85M ≥ 1975 =>
M ≥ 1975/85 => M ≥ 23.23 => M= 24
When we replace value for M in the second inequality we get
B ≤ 4*24 => B ≤ 96
We will check 25 * 24 + 15 * 96 = 600 + 1440 = 2040$ ≥ 1975$
That is correct!
If we accept M= 23 then B≤ 92
We will check again 25*23 + 15*92 = 575 + 1380 = 1955$ ≤ 1975$
That is incorrect!
Good luck!!!