The average of five consecutive integers is 22. What is the same of the largest and the smallest of the integers?
a. 11
b. 22
c. 45
d. 66
e. 88

Question

The average of five consecutive integers is 22. What is the same of the largest and the smallest of the integers?
a. 11
b. 22
c. 45
d. 66
e. 88

aveline · Answer

$$\frac{ (x)+(x+1)+(x+2)+(x+3)+(x+4) }{ 5 }=22$$

xxuan · Answer

5x + 10 = 110 => x = 20 ???

aveline · Answer

$$\frac{ 5x+10 }{ 5 }=22$$$$x+2=22$$
$$x=20$$
This means that your integers are 20, 21, 22, 23, and 24.

xxuan · Answer

I don't know why my teacher answer is C.

welshfella · Answer

should same =  'sum'

phi · Answer

*** What is the same of the largest and the smallest of the integers?****
I assume the should read  *sum* of the largest and smallest, which would be 20+24= 44

choice C is the closest, but it looks like a typo.

welshfella · Answer

yea

phi · Answer

btw, symmetry can make the arithmetic simpler:
let "x" be the *middle* number, then the 5 numbers would be 
x-2, x-1, x , x+1, x+2
and the sum would be 5x  (notice how the numbers cancel)
and the average
5x/5 =22  gives
x= 22  (remember, this is the middle number)

the sum of the low and high is  x-2+x+2 = 2x
so the answer is 2*22 = 44