Find all the pairs of consecutive even positive integers both of which are greater than 10 and their sum is less than 50

To find all pairs of consecutive even positive integers, both of which are greater than 10 and their sum is less than 50, we can proceed as follows:

Let the consecutive even integers be \( x \) and \( x + 2 \).

Given:
1. Both integers are greater than 10.
2. Their sum is less than 50.

The conditions can be expressed as:
\[ x > 10 \]
\[ x + (x + 2) < 50 \]

Simplify the inequality:
\[ 2x + 2 < 50 \]
\[ 2x < 48 \]
\[ x < 24 \]

So, \( x \) must satisfy:
\[ 10 < x < 24 \]

Since \( x \) must be an even integer, the possible values for \( x \) are:
\[ 12, 14, 16, 18, 20, 22 \]

We can now form the pairs by adding 2 to each of these values:

1. \( x = 12 \): The pair is (12, 14)
2. \( x = 14 \): The pair is (14, 16)
3. \( x = 16 \): The pair is (16, 18)
4. \( x = 18 \): The pair is (18, 20)
5. \( x = 20 \): The pair is (20, 22)
6. \( x = 22 \): The pair is (22, 24)

Thus, the pairs of consecutive even positive integers both of which are greater than 10 and whose sum is less than 50 are:

\[
(12, 14), (14, 16), (16, 18), (18, 20), (20, 22), (22, 24)
\]

Would you like any more details or have any questions?

Here are five more questions you can ask:
1. How do you solve a quadratic equation using the quadratic formula?
2. What is the process to find the derivative of a polynomial function?
3. Can you explain how to integrate by parts with an example?
4. How do you determine the limit of a function as it approaches a specific point?
5. What are the properties of definite integrals and how are they applied?

**Tip:** When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number.

Discover how to find pairs of consecutive even positive integers both greater than 10 with a sum less than 50. This problem involves number theory and inequalities, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation