Question

How do you find four consecutive odd integers such that three times the sum of the first and second is 25 less than the fourth?

Answer 1

First, to set up consecutive odd or even integers you have to add 2 to the previous integer.
Let x be the first integer,
(x + 2), (x + 4), and (x + 6)

Now set up the parameters they give:
3(x + x + 2) = x + 6 - 25
Solving:
Combine like terms and distribute on the left, combine like terms on the right.
3(2x + 2) = x - 19
6x + 6 = x - 19
Subtract x from both sides and subtract 6 from both sides.
5x = -25
Divide both sides by 5
x = -5
x + 2 = -5 + 2 = -3
x + 4 = -5 + 4 = -1
x + 6 = -5 + 6 = 1
Check:
3(-5 + -3) ?=? 1 - 25
-24 ?=? -24 CORRECT