Q18. - Algebra 2

Question

The average (arithmetic mean) of the test scores of a class of x  students is 74, and the average of the test scores of a class of y students is 88. When the scores of both classes are combined, the average is 76. What is the value of $\frac{x}{y}$?

Step-by-Step Solution

Answer

The value of $\frac{x}{y}=\frac{6}{1}$.

Step 1 – Find a total points of x  and  y .

The average mean of the test score of a class of x students is 74.

So, the total points of x students is 74x.

 

The average mean of the test score of a class of y students is 88.

So, the total points of $y$students is 88y.

 

The average mean of the test scores of both classes when combined is 76.

So, the total points of $x+y$ students is $76\left(x+y\right)$.

Step 2 – Find an equation for x  and  y :

The total grand points of x and  y is equal to the total grand points of sum of x and y

 

This can be mathematically written as follows:

$74x+88y=76\left(x+y\right)$

Step 3 – Solve the equation for x y :

Solve $74x+88y=76\left(x+y\right)$as follows:

$\begin{array}{c}74x+88y=76\left(x+y\right)\\ 74x+88y=76x+76y\\ 88y-76y=76x-74x\\ 12y=2x\\ \frac{12}{2}=\frac{x}{y}\\ \frac{6}{1}=\frac{x}{y}\end{array}$

So, the value of $\frac{x}{y}=\frac{6}{1}$.