Question

The average of the numbers 5, 7, 2, 6, x (x+1),7 is 5 find the value of x​

Answer 1

Answer as a fraction: x = 7/2

Answer as a decimal: x = 3.5

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Work Shown:

n = sample size = number of values

n = 7

S = sum of the values

S = 5 + 7 + 2 + 6 + (x+1) + (x) + 7

S = 2x+28

Dividing S over n will get us the average, which in this case is 5

S/n = average

(2x+28)/7 = 5

2x+28 = 7*5

2x+28 = 35

2x = 35-28

2x = 7

x = 7/2 which is the answer in fraction form

x = 3.5 which is the answer in decimal form

The decimal value is exact without any rounding.

Answer 2

3.5

Explanation:

So the average of numbers can be defined as:
`average=(sum)/(amount)`

In other words, (the sum of numbers) / (the amount of numbers)

In our case, there is 7 numbers. The sum can be written as:
`5+7+2+6+x+(x+1)+7`

Adding like terms we get:
`28+2x`

Now combing the sum and amount we get the fraction:
`(28+2x)/(7)`

Since we're given the average, we can set that equal to our expression to solve for x:

`5=(28+2x)/(7)`

No all we do is use some basic algebraic properties

Original Equation:

`5=(28+2x)/(7)`

Multiply both sides by 28

`35 = 28+2x`

Subtract 28 from both sides

`7=2x`

Divide both sides by 2x

`3.5=x`