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

Answer:average of new list is 94

Step-by-step explanation:

Average = sum of numbers/ total number of numbers

Let the original list contain x,y,z and 80

Average = 90

Numbers = 4

Average of original list

=(x+y+z+80)/4=90

x+y+z+80= 360

x+y+z=280

Let (x+y+z) = b

b = 280

The new list has 4 numbers and the same first 3 numbers as the original list, but the the fourth number in the new list is 96.

That means the sum of the first 3 numbers, (x+y+z) which equals b in the original list is same as the sum of the first 3 numbers in the new list

Let average of the new list be a

Average of new list

=(b +96 )/4 =a

b +96 = 4a

b = 4a-96

Since b in original list = b in new list

4a-96 = 280

4a = 280+96=376

a = 376/4 =94

Answer 2

Answer:

the average of this new list of numbers is 94

Step-by-step explanation:

Hello!

To answer this question we will assign a letter to each number for the first list and the second list of numbers, remembering that the last number of the first list is 80 and the last number of the second list is 96

for the first list

$\frac{a+b+c+80}{4} =90$

for the new list

$\frac{a+b+c+96}{4} =X$

To solve this problem consider the following

1.X is the average value of the second list

2. We will assign a Y value to the sum of the numbers a, b, c.

a + b + c = Y to create two new equations

for the first list

$\frac{y+80}{4} =90$

solving  for Y

Y=(90)(4)-80=280

Y=280=a+b+c

for the second list

$\frac{y+96}{4} =X$

$\frac{280+96}{4} =X\\x=94$

the average of this new list of numbers is 94