Answer:
[tex]L = 30\\R = 21\\M = 42[/tex]
Step-by-step explanation:
Let's assign each person a variable using the first letter of his/her name.
Then we get the following equations based on the information given:
[tex]L + M + R = 93\\L - 9 = R\\M = 2R[/tex]
Then we can use substitution:
[tex]L + M + R = 93\\L + (2R) + R = 93\\L + 3R = 93[/tex]
Rearrange the second equation:
[tex]L - R = 9[/tex]
Multiple the equation by 3:
[tex]3L - 3R = 27[/tex]
Combine the equations to solve for a single variable (L):
[tex]L + 3L = 4L\\3R - 3R = 0\\93 + 27 = 120[/tex]
Then we have a new equation:
[tex]4L = 120\\L = 30[/tex]
Use substitution to get the rest:
[tex]L - 9 = R\\(30) - 9 = R\\R = 21\\\\M = 2R\\M = 2(21)\\M = 42[/tex]
