Three numbers of the combination for a lock are consecutive integers, and the sum is 42. Find the combination

Answer 1

Let us assume that the first number is x.

Since the three numbers are consecutive integers, the other two numbers would be x+1 and x+2.

The sum of the three integers is 42:

x + (x+1) + (x+2) = 42

3x+3 = 42

3s = 39

x = 13

The three consecutive numbers are 13, 14 & 15.

Answer 2

First we need to dissect some of the vocabulary here. Consecutive means that the numbers are right next to each other on a number line (like 1, 2, 3) and integers are whole counting numbers (so they aren't decimals or fractions). This helps us create a representation for these numbers.

Since we don't know the first of these 3 consecutive numbers, we can represent the first one as N. The next consecutive number will be one whole number about N, so we can call this N+1. For the same reason we can call the third number N+2.

So we have N, N+1, and N+2. The only other piece of info we have on these is that they have a sum of 42. In other words, if we add them all up it will equal 42. So can create an equation by doing just this.

Now we have N+N+1+N+2=42. We can collect all like terms to simplify this. By collecting the N terms and the constant number terms on the left hand side we get 3N+3=42. Now we need to solve for N by moving all the other numbers to the right side.

First subtract 3 from both sides and get 3N=39. Then divide both sides by 3 and get N=13.

Since we now know N, we can go back to our list of N, N+1, N+2 to find the other 2 consecutive numbers.