The sum of three consecutive integers is 31 more than the largest integer. find the integers

To solve with an equation, let's call the three consecutive integers g, g+1, and g+2.

So, (g)+(g+1)+(g+2)=(g+2)+31

3g + 3 = g + 33

2g = 30

g = 15

The integers are 15, 16, and 17.

To check:

The sum of 15, 16, and 17 is 48. 17 + 31 is also 48.

Let's express this in algebraic terms:

The expressions for the integers and respective values are expressed below:

Now, to check, we apply the original problem and the values we discovered:

We are right, so:

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step-by-step explanation: