Question

17. If a + 2b = 14 and 5a + 4b = 16,
what is the average (arithmetic
mean) of a and b? ​

Answer 1

Step-by-step explanation:

a+2b=14. (1)

5a+4b=16. (2)

a=14-2b put this value in equation (2),

5(14-2b)+4b=16

70-10b+4b=16

-6b=16-70

-6b= -54

b=54/6

b=9

put value of b in equation (1),

a+2(9)=14

a=14-18

a= -4

hence a= -4 and. b= 9

mean=(a+b)/2

=(-4+9)/2

=5/2

Answer 2

Answer:

Average (arithmetic mean) of a and b is 2.5.

Step-by-step explanation:

$a + 2b =14---(i)\\5a + 4b = 16---(ii)\\a=14-2b----(iii)$

Putting the equation (iii) in (ii), we get

$5(14-2b)+4b=16\\70-10b+4b=16\\-6b=16-70\\b=\frac{-54}{-6}\\ b=9$

Putting value of b in equation (i)

$a + 2(9)=14\\a+18=14\\a=14-18\\a=-4$

a = -4

b = 9

Average of a and b  $=\frac{a+b}{2}$

$=\frac{-4+9}{2}\\ =\frac{5}{2}\\ = 2.5$

Average (arithmetic mean) of a and b is 2.5.

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