Can you help me find the average of the new list of numbers?

Question

The Average of a list of 4 numbers is 90.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 80, and the fourth number in the new list is 96. What is the average of this New list of numbers?

Answer 1

Let x is sum of 1st 3 numbers and y is 4th number; y is forth number.

Then (x + 80)/4 = 90; so, x = 360 - 80 = 280. Now (280 + 96)/4 = 94.

94 is new average.

Answer 2

the original list, the average is 90 and the 4th number is 80:

(num1 + num2 + num3 + 80)/ 4 = 90

num1 + num2 + num3 + 80 = 360 <--- multiplies both sides by 4

num1 + num2 + num3 = 280 <--- subtracts 80 from both sides

so the sum of the first three numbers is 280

the new list, the 4th number is 96 and the first 3 numbers are the same:

(num1 + num2 + num3 + 96)/4 =

((num1 + num2 + num3) + 96)/4 <--- associative property

(280 + 96)/4 <--- substitution

376/4 =

94

the new average is 94