SOLUTION: the sum of four consecutive odd numbers is 128. Then the smallest number is?

Question 807894: the sum of four consecutive odd numbers is 128. Then the smallest number is?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x be an integer

So 2x is always even

Forcing 2x + 1 to always be odd

The next odd number after that is (2x+1)+2 = 2x + 3

The next odd number after that is (2x+3)+2 = 2x + 5

The next odd number after that is (2x+5)+2 = 2x + 7

=======================================================

Add up the four integers. Then set this sum equal to 128

(2x+1)+(2x+3)+(2x+5)+(2x+7) = 128

2x+1+2x+3+2x+5+2x+7 = 128

8x+16 = 128

8x = 128-16

8x = 112

x = 112/8

x = 14

=======================================================

Since x = 14, we know

2x+1 = 2*14 + 1 = 29

2x+3 = 2*14 + 3 = 31

2x+5 = 2*14 + 5 = 33

2x+7 = 2*14 + 7 = 35

So the four consecutive odd integers are: 29, 31, 33, 35

The smallest number is 29
RELATED QUESTIONS
The sum of four consecutive odd integers is greater than 24.Determine the first four in (answered by josgarithmetic)

The sum of four consecutive numbers is 10 times the smallest number. Find the four... (answered by CubeyThePenguin)

the sum of four consecutive odd integers is 128 find the four... (answered by Fombitz,Alan3354)

If (p-3) is the largest if four consecutive odd numbers,then the smallest is (answered by stanbon)

the sum of four consecutive odd numbers is 64. what is the largest... (answered by rvfer)

The sum of three consecutive odd numbers is 69. What is the smallest of these... (answered by Stitch)

The sum of three consecutive odd numbers is 63. What is the smallest of these... (answered by fractalier)

the sum of three consecutive odd numbers is 75 what are the smallest of these... (answered by Alan3354)

The sum of three consecutive odd numbers is 47. What are the smallest of these... (answered by Alan3354)