There are three consecutive integers such that the sum of the first number, two times the second number, and five less than the third number equals 203. What is the second number in the sequence?

Answer 1

The three consecutive integers may be (x), (x+1), and (x+2). If you choose to use that method, then, once you find the value of x, you must answer the question, "What is the second number in the sequence?" If you get rushed, you may forget this important step.

The three consecutive integers may be (x-1), (x), and (x+1). The value of x is the answer.

(x-1) + 2*(x) + ( (x+1) - 5 ) = 203

4x -5 = 203

4x = 208

x = 52

Check:

Is 51 + 2*52 + (53-5) = 203 ?

51 + 104 + 48 = 204 ?

203 = 203 ?yes

Answer 2

Let's call the numbers a, b, and c. Since they're consecutive integers, we can express the first and third numbers relative to the second one:

a = b - 1, and c = b + 1.

Now let's translate your sentence into an equation, reading left-to-right:

a + 2b + (c - 5) = 203,

or, substituting our expressions for a and c,

b - 1 + 2b + (b + 1 - 5) = 203.

Simplify and solve:

4b -5 = 203

4b = 208

b = 52.