Question

Three maths classes: X, Y, and Z take an algebra test. The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and the average score of class Y and Z is 81. What is the average score of classes X, Y, and Z?

Options

• 81.5

• 80.5

• 83

• 78

Answer 1

81.5

Explanation:

According to question

(i)  `(83"x"+76"y")/("x+y")=79`

`⇒"x"=(3"y")/4`

(ii)  `(76"y"+85"z")/("y+z")=81`

`"Z"=(5"y")/4`

Average of all 3`=(83"x"+76"y"+85"z")/("x+y+z")`

`=(83((3"y")/4)+76"y"+85((5"y"))/4)/((3"y")/4+"y"+(5"y")/4)`

`⇒(249/4+76+425/4)/(3//4+1+5//4)`

`=((249+304+425)/4)/((3+4+5)/4)=978/12=81.5`