find three consecutive odd integers such that four times the first decreased by the second is 13 more than twice the third

Answer 1

find three consecutive odd integers: Since these are odd and consecutive, they must increase by 2 (Think of odd numbers such as 1, 3, 5, 7. They increase by 2). So, let the first one be x, then the others are x+2 and x+4

such that four times the first: 4*x

decreased by the second: -(x+2) [Note that the second one is x+2]

is: 4*x-(x+2) =

13 more than twice the third: 13 + 2*(x+4)

4x - (x+2) = 13 + 2(x+4)

3x + 2 = 13 + 2x + 4

3x + 2 = 17 + 2x (subtract 3x from both sides)

x + 2 = 17 (subtract 2 from both sides)

x = 15

Check that it is an odd number.

So, the three consecutive odd numbers are 15, 17, and 19.