Question

The mean of 5 consecutive integers is 19. What is the difference between the largest and the smallest of the 5 integers?

Answer 1

Hey friend!

Here is your answer:



Let the five consecutive integers be x, x +1, x + 2, x + 3, x + 4

According to the question,
[x + (x + 1) + (x + 2) + (x + 3) + (x + 4)] /5 = 19

=> (5x + 10)/5 = 19

=> x + 2 = 19

=> x = 17

Now, difference between the largest and smallest integer from the five integers is x + 4 - x = 4



I hope it helps

Answer 2

Answer:

$difference \: between \: the \: largest \: and \: the \: smallest \: is \: 4.$

Step-by-step explanation:

$let \: 5 \: consecutive \: integers \: be \\ x, \: (x + 1), \: (x + 2), \: (x + 3) \: and \: (x + 4). \\mean \: of \: 5 \: consecutive integers \: is \: 19 \\ </p><p>Therefore \\ \frac{x + (x + 1) + (x + 2) + (x + 3) + (x + 4)}{5} = 19 \\ Therefore \\ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = (5)(19) \\ 5x + 10 = (5)(19) \\ 5(x + 2) = 5(19) \\ x + 2 = 19 \\ x = 17 \\ Here \: smallest \: integer \: is \: x \: and \: largest \: integer \: is \: (x + 4) \\ Therefore \\ x + 4 = 17 + 4 = 21 \\ difference \: between \: the \: largest \: and \: the \: smallest: \\ (x + 4) - (x) = 4 \\ Therefore \: difference \: between \: the \: largest \: and \: the \: smallest \: is \: 4$