Math Problem Statement
Find the value of x if the arithmetic means of 3 and 3×+5 is 8
Solution
To solve for , we are given that the arithmetic mean of 3 and is 8. The formula for the arithmetic mean of two numbers and is:
Here, and , and the arithmetic mean is given as 8. So, we set up the equation:
Now, simplify and solve for :
Multiply both sides of the equation by 2 to eliminate the denominator:
Subtract 8 from both sides:
Now, divide by 3:
Thus, the value of is .
Would you like more details, or do you have any questions?
Here are 5 related questions to expand your understanding:
- What is the arithmetic mean of two other variables, and , if the sum of their arithmetic means equals 10?
- How would the solution change if the arithmetic mean given were a different number?
- Can you solve for if the arithmetic mean of 4 and is 6?
- What is the formula for the arithmetic mean of three numbers?
- How can arithmetic means be used to solve problems in statistics?
Tip: Always check your final answer by plugging it back into the original equation to ensure it satisfies the condition.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Mean
Linear Equations
Formulas
Arithmetic Mean Formula: (a + b) / 2
Basic Linear Equation Solving
Theorems
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Suitable Grade Level
Grades 6-8
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