The average (arithmetic mean) of two numbers is 12. if the smaller of the two numbers is 6 less than the other number, what is the value of the larger number?

15

Step-by-step explanation:

What is average/arithmetic mean?

It means the "sum of the numbers" divided by the "number of numbers".

Let the two numbers be "x" & "y"

It says, average of 2 numbers is 12, so we can write:

Smaller number is 6 less than bigger number. Let's suppose x is the bigger one and y is the smaller one, so we can write:

x - 6 = y

Now we have 2 equations:

x + y = 24

x - 6 = y

Putting 2nd in 1st we get:

x + x - 6 = 24

Solving for x:

2x - 6 = 24

2x = 24 + 6

2x = 30

x = 30/2

x = 15

Now we know y = x - 6, so

y = 15 - 6 = 9

y = 9

The larger number is 15

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