Answer:
The average of x and y is 95.
Step-by-step explanation:
Given : If the average (arithmetic mean) of x, y, and 20 is 10 greater than the average of x, y, 20, and 30.
To find : What is the average of x and y?
Solution :
Average is the sum of observation divided by number of observation.
According to question,
[tex]\frac{x+y+20}{3}=10+(\frac{x+y+20+30}{4})[/tex]
[tex]\frac{x+y+20}{3}=\frac{40+x+y+20+30}{4}[/tex]
[tex]\frac{x+y+20}{3}=\frac{x+y+90}{4}[/tex]
[tex]4(x+y)-3(x+y)=3(90)-20(4)[/tex]
[tex]x+y=190[/tex]
Divide equation by 2,
[tex]\frac{x+y}{2}=\frac{190}{2}[/tex]
[tex]\frac{x+y}{2}=95[/tex]
Therefore, the average of x and y is 95.
