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Chapter 3: Q18. (page 151)

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 xy?

Short Answer

Expert verified

The value of xy=61.

Step by step solution

01

– 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 ystudents is 88y.

The average mean of the test scores ofboth classeswhen combined is 76.

So, the total points of x+ystudents is 76x+y.

02

– 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=76x+y

03

– Solve the equation for xy:

Solve 74x+88y=76x+yas follows:

74x+88y=76x+y74x+88y=76x+76y88y鈭�76y=76x鈭�74x12y=2x122=xy61=xy

So, the value of xy=61.

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