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The sum of three consecutive integers is $96,$ find the three integers.

$$\{31,32,33\}$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

00:47

Set up an algebraic equati…

01:24

The sum of three consecuti…

02:03

Find three consecutive int…

03:18

Find four consecutive even…

00:50

00:42

01:00

00:46

The sum of the first and t…

01:09

Solve each number word pro…

01:28

Solve each problem involvi…

00:54

we have the following problem where we're trying to find out the some consecutive integers and we're getting the fact that three consecutive vintages at up to 96 we want to know what are those three consecutive integers? So we're gonna have to organize a linear equation here because we're gonna have X value raised to the power of one. You're gonna use the fact that addition and subtraction under each other in multiplication division, also under each other. So how do we solve this one? We know that three consecutive integers out up to 96. Yeah, so in two years, or just whole numbers and consecutive means that gets bigger by one. So we have we're gonna start with one value X that we don't know, and then we're gonna add one to the value because it's consecutive. And then we're gonna have a third number because there's three that's gonna be X and plus one plus one. So we have our first unknown integer X plus. Our second and teacher is simply going to be X plus one on our third in picture is gonna be just X plus one plus one plus one. Still So this one is exposed to and the radical to 96 So we can simplify this a little bit. We're basically just gonna have combine the excess and the one plus two. So we have three eggs, plus free equals six. You know, you want to get exploit. So if we want to solve X well, in this case, X is gonna be Well, we have to get out of this. Three over here, minus three was 96 minus three. So now we're gonna have three X equal to and three mhm. And now we want to get expert itself. So we're gonna divide both sides of the equation by three 93 divided by three. So now we have X is equal to pretty one on the left side, three divided by three is just 11 time. Sex is just acts and the 93 divided by three is simply 31. So our first integer X is 31 and then our second integer is gonna be 31 plus one is 32 and then our third integer is X plus two. It's gonna be 33. All of these value all of these numbers added up together it's gonna add up to 96. So these are our three consecutive integers

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