Question

Consider the following 8 numbers, where one labelled x is unknown. 4, 32, 6, x , 10, 3, 35, 37 Given that the range of the numbers is 64, work out 2 values of x

Answer 1

Answer:

$\boxed{x=-27, \: x=67}$

Step-by-step explanation:

There can be two values of x.

The range is largest no. - smallest no.

Range = 64

Let x be the smallest no.

largest no. from the list is 37

37 - x = 64

-x = 64 - 37

x = -27

Let x be the largest no.

smallest no. from the list is 3

x - 3 = 64

x = 64 + 3

x = 67

Answer 2

The needed two values of x are: 67 and -27.

Given sequence of 8 numbers as:

$4, 32, 6, x, 10, 3, 35, 37$

Given range of above sequence: 64

The range of a sequence is defined as the difference between the maximum and minimum value of the sequence.

Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that  the range remains at 64.

Case 1: x as minimum value of given sequence:

If so, then the maximum value is 37. Then-

$range = maximum \:value - minimum \:value\\or\\64 = 37-x\\or\\x = -27$

Case 2: x as maximum value of the given sequence:

If so, then the minimum value of the sequence is 3. Then-

$range = maximum \:value - minimum \:value\\or\\64 = x - 3\\or\\x = 67$

Thus the needed two values of x are: 67 and -27.

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