Answer:
a is 42.5
b is 5
Step-by-step explanation:
the mean of: a, a, b is 30
[tex] \frac{a + a + b}{3} = 30[/tex]
[tex] \frac{2a + b}{3} = 30[/tex]
multiply 3 on both sides
[tex]2a + b = 90[/tex]
the mean of a, a, b, b, b, is 20
[tex] \frac{a + a + b + b + b}{5} = 20[/tex]
[tex] \frac{2a + 3b}{5} = 20[/tex]
multiply 5 on both sides
[tex]2a + 3b = 100[/tex]
solve both equations simultaneously
[tex]2a + b = 90 [/tex]
[tex]2a + 3b = 100[/tex]
subtract across. 2a-2a=0, b-3b= -2b, 90-100= -10
[tex] - 2b = - 10[/tex]
[tex]b = 5[/tex]
go back to one of the equations and substitute b=5 back in to find a
[tex]2a + b = 90[/tex]
[tex]2a + 5 = 90[/tex]
subtract 5 on both sides
[tex]2a = 85[/tex]
divide 2
[tex]a = 42.5[/tex]
so a is 42.5 and b is 5
