Question

The sum of three consecutive odd integers is 76 less then seven times the middle number.Find three integers

Answer 1

The sum of three consecutive odd integers is 76 less then seven times the middle number. The three integers are 17, 19 and 21 respeectively

Solution:

Since each consecutive odd integer is separated by a difference of  2

Let "n" be the first integer

n + 2 be the second integer

n + 4 be the third integer

Given that the sum of three consecutive odd integers is 76 less then seven times the middle number

Which means,

The sum of ( n, n + 2, n + 4) is equal to 76 less than seven times the middle number ( 7(n + 2))

That is,

n + n + 2 + n + 4 = 7(n + 2) - 76

3n + 6 = 7n + 14 - 76

4n = 68

n = 17

So we get:

First integer = n = 17

Second integer = n + 2 = 17 + 2 = 19

Third integer = n + 4 = 17 + 4 = 21

Thus the three consecutive odd integers are 17, 19 and 21 respeectively