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the mean of: a, a, b is 30

the mean of a, a, b, b, b, is 20
find the values of a and b

Sagot :

belisa2020kgi

a+b = 40

Step-by-step explanation:

Mean of a and b is [math]\frac{a+b}{2} = 20[/math]

[math]

SpiritInly

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

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