Three Consecutive Integers Add up to 51. What are these Integers?

Solution for Three Consecutive Integers Add up to 51. What are these Integers?

The problem states that there are three consecutive integers, which means numbers that follow each other in sequence without any gaps, such as 1, 2, 3 or 5, 6, 7.

Setting up Equations:

Let's call the first integer x. Since the integers are consecutive, the next two integers will be x + 1 and x + 2. The problem also tells us that these three integers add up to 51.

We can write the equation to represent this situation as

x+(x+1)+(x+2)=51.

Solving the Equation:

Combine like terms to simplify the equation:

3x+3=51.

Subtract 3 from both sides:

3x=48.

Divide by 3:

x=16.

Finding the Integers:

Now that we have the value of x, we can find the three consecutive integers. They are

x=16, x+1=17, and x+2=18.

Therefore, the three consecutive integers that add up to 51 are 16, 17, and 18.

This problem involves basic algebraic concepts and is solved by setting up and solving an equation to find the unknown values.

Consecutive Integers and Sums

Understanding problems involving consecutive integers and their sums is a common concept in mathematics, especially in algebra.

Consecutive Integers:

Consecutive integers are numbers that follow each other in order without any gaps. For example, 3, 4, and 5 are consecutive integers because they come one after the other.

Problem Setup:

When dealing with problems like "Three Consecutive Integers Add up to 51," we can represent the consecutive integers as x, x + 1, and x + 2, where x is the first integer.

Equation Formation:

To find the integers, we set up an equation based on the information given. In this case, the sum of the three consecutive integers is given as 51, so we write the equation x+(x+1)+(x+2)=51.

Solving the Equation:

We solve the equation by combining like terms and simplifying it to find the value of x. Once we have x, we can determine the consecutive integers by adding 1 and 2 to x.

Application of Algebra:

This type of problem involves basic algebraic principles such as combining terms, isolating variables, and solving equations. It's a fundamental skill in mathematics that helps in solving various real-world problems involving number patterns.

Understanding Patterns:

By understanding how consecutive integers work and how their sums can be calculated, we can apply this knowledge to solve similar problems involving different sets of consecutive numbers and their sums.

What are Consecutive Integers?

Consecutive integers are numbers that follow each other in order without any gaps between them. For instance, 3, 4, and 5 are consecutive integers because they come one after the other. In problems where we are given that three consecutive integers add up to a certain number, like 51, we use algebra to solve for these integers. We represent the first integer as x. Then, the next two consecutive integers are x + 1 and x + 2.

When we talk about consecutive integers in mathematics, we often use them to describe sequences or patterns of numbers. These sequences can go in either direction, such as counting up from a starting point or counting down from a higher number. For instance, if you start counting from 1 and go up by 1 each time, you'll have a sequence of consecutive integers: 1, 2, 3, 4, and so on.

Consecutive integers are also used in various mathematical problems and equations. For example, if you're asked to find three consecutive integers that add up to a certain number, you would represent the first integer as x, the second as x + 1 (since it comes right after x), and the third as x + 2 (the next number after x + 1). This approach helps in solving problems where the relationship between numbers follows a consistent pattern of consecutive order.