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 average score of class $Y$ and $Z$ is $81$. What is the average score of classes $X,Y$ and $Z$?

• A. $81.5$
• B. $80.5$
• C. $83$
• D. $78$

Answer 1

Answer: (A)

$81.5$

According to question
(i) $\frac{83x+76y}{x+y}=79$
$\Rightarrow x=\frac{3y}{4}$
(ii) $\frac{76y+85z}{y+z}=81$
$Z=\frac{5y}{4}$
Average of all $3=\frac{83x+76y+85z}{x+y+z}$
$=\frac{83\left(\frac{3y}{4}\right)+76y+85\frac{\left(85\right)}{4}}{\frac{3y}{4}+y+\frac{5y}{4}}$
$\Rightarrow \frac{\frac{249}{4}+76+\frac{425}{4}}{\frac{3}{4}+1+\frac{5}{4}}$
$=\frac{\frac{249+304+425}{4}}{\frac{3+4+5}{4}}=\frac{978}{12}=81.5$.