Answer:
[tex]\left \{ {y\leq 25-x} \atop {y\geq 3x}} \right.[/tex]
The graph is attached.
Step-by-step explanation:
Let be "x" the number of metamorphic samples and "y" the number of sedimentary samples.
You know that you want to  to have at most 25 samples, then:
[tex]y\leq 25-x[/tex]
And you want to have at least 3 times as many sedimentary samples as
metamorphic samples, then:
[tex]y\geq 3x[/tex]
Therefore, the system of  inequalities that model the situation is:
[tex]\left \{ {y\leq 25-x} \atop {y\geq 3x}} \right.[/tex]
The y-intercept of the line [tex]y=25-x[/tex] is:
[tex]y=25-(0)\\\\y=25[/tex]
And the x-intercept is:
[tex]0= 25-x\\\\x=25[/tex]
Knowing this, you can graph the line
The y-intercept of the line [tex]y= 3x[/tex] is:
[tex]y=3(0)\\\\y=0[/tex]
And the x-intercept is:
[tex]0= 3x\\\\x=0[/tex]
Knowing this, you can graph the line.
Observe the graph attached, where the solution of the system of inequalities is the intersection of the regions.
