ClassX Video Lessons Subjects Algebra Solving a consecutive integer problem algebraically | Linear equations | Algebra I
In this article, we will learn how to find four consecutive odd numbers that add up to 136. We’ll break down the steps to solve this math problem in a fun and easy way!
First, let’s understand what consecutive odd integers are. These are odd numbers that come one after another. For example, if you start with 3, the next consecutive odd numbers would be 5, 7, and 9. Another example is starting with 11, which leads to 13, 15, and 17.
It’s important to remember that numbers like 3 and 7 are not consecutive because there are even numbers (4 and 6) between them. Consecutive odd numbers skip the even numbers in between.
To solve the problem, let’s say the smallest of these four numbers is x. The next three numbers can be written like this:
So, the four consecutive odd numbers are x, x + 2, x + 4, and x + 6.
According to the problem, the sum of these four numbers is 136. We can write this as an equation:
x + (x + 2) + (x + 4) + (x + 6) = 136
Let’s simplify this equation by combining like terms:
4x + 12 = 136
To find x, we first subtract 12 from both sides of the equation:
4x = 136 – 12
4x = 124
Next, we divide both sides by 4 to solve for x:
x = 124 / 4 = 31
Now that we know x is 31, we can find the four consecutive odd numbers:
So, the four consecutive odd numbers are 31, 33, 35, and 37.
In conclusion, we found the four consecutive odd numbers that add up to 136. By understanding how consecutive odd numbers work and setting up a simple equation, we solved the problem easily. Now you know how to tackle similar math challenges!
Draw a number line on a large sheet of paper. Mark and label the consecutive odd numbers starting from 1 up to 50. Use this number line to visually identify sets of four consecutive odd numbers. This will help you understand the concept of consecutive odd integers better.
Write down the equation x + (x + 2) + (x + 4) + (x + 6) = 136 on a piece of paper. Cut the equation into separate parts (e.g., x, + 2, = 136, etc.). Mix them up and challenge yourself or a classmate to rearrange the pieces to form the correct equation.
Go on a scavenger hunt around your classroom or home to find objects that can be grouped into sets of four consecutive odd numbers. For example, find 31 pencils, 33 erasers, 35 paper clips, and 37 rubber bands. This activity will reinforce the concept of consecutive odd numbers in a fun way.
Write a short story or comic strip that involves characters or objects represented by the numbers 31, 33, 35, and 37. Explain how these numbers are connected and why they are important in your story. Share your story with the class to demonstrate your understanding of consecutive odd integers.
Create a quiz using an online platform like Kahoot or Google Forms. Include questions about finding consecutive odd integers, setting up equations, and solving for x. Invite your classmates to participate and see who can solve the problems the fastest.
Consecutive – Following one after another in order without gaps – Example sentence: In the sequence 2, 4, 6, 8, the numbers are consecutive even numbers.
Odd – Numbers that are not divisible by 2 – Example sentence: The numbers 1, 3, 5, and 7 are examples of odd numbers.
Integers – Whole numbers that can be positive, negative, or zero – Example sentence: The set of integers includes -3, 0, and 4.
Numbers – Symbols or words used to represent a quantity – Example sentence: In mathematics, numbers like 5, 10, and 15 are used to count or measure.
Equation – A mathematical statement that shows the equality of two expressions – Example sentence: The equation 3x + 5 = 11 can be solved to find the value of x.
Solve – To find the value of a variable that makes an equation true – Example sentence: To solve the equation 2x = 10, divide both sides by 2 to find x = 5.
Sum – The result of adding two or more numbers together – Example sentence: The sum of 4 and 6 is 10.
Smallest – The least in size, amount, or degree – Example sentence: Among the numbers 3, 7, and 9, the smallest is 3.
Terms – Parts of an algebraic expression separated by addition or subtraction – Example sentence: In the expression 5x + 3y – 7, the terms are 5x, 3y, and -7.
Simplify – To reduce an expression to its simplest form – Example sentence: To simplify the expression 4x + 2x, combine like terms to get 6x.
