Answer:
[tex]L = 43[/tex] and [tex]M = 47[/tex]
Step-by-step explanation:
Given
[tex]L = 2x + 25[/tex]
[tex]M = 4x + 11[/tex]
Required
Determine the values of L and M
Since L and M are complementary, we have that
[tex]L + M = 90[/tex]
Substitute values for L and M
[tex]2x + 25 + 4x + 11 = 90[/tex]
Collect Like Terms
[tex]2x + 4x = 90 - 11 - 25[/tex]
[tex]6x = 54[/tex]
Divide both sides by 6
[tex]x = \frac{54}{6}[/tex]
[tex]x = 9[/tex]
Substitute 9 for x in the expressions of L and M
[tex]L = 2x + 25[/tex]
[tex]L = 2 * 9 + 25[/tex]
[tex]L = 18 + 25[/tex]
[tex]L = 43[/tex]
[tex]M = 4x + 11[/tex]
[tex]M = 4 * 9 + 11[/tex]
[tex]M = 36 + 11[/tex]
[tex]M = 47[/tex]
