Math Problem Statement

Find the value of x if the arithmetic means of 3 and 3×+5 is 8

Solution

To solve for xx, we are given that the arithmetic mean of 3 and 3x+53x + 5 is 8. The formula for the arithmetic mean of two numbers aa and bb is:

Arithmetic Mean=a+b2\text{Arithmetic Mean} = \frac{a + b}{2}

Here, a=3a = 3 and b=3x+5b = 3x + 5, and the arithmetic mean is given as 8. So, we set up the equation:

3+(3x+5)2=8\frac{3 + (3x + 5)}{2} = 8

Now, simplify and solve for xx:

3+3x+52=8\frac{3 + 3x + 5}{2} = 8

8+3x2=8\frac{8 + 3x}{2} = 8

Multiply both sides of the equation by 2 to eliminate the denominator:

8+3x=168 + 3x = 16

Subtract 8 from both sides:

3x=83x = 8

Now, divide by 3:

x=83x = \frac{8}{3}

Thus, the value of xx is 83\frac{8}{3}.

Would you like more details, or do you have any questions?


Here are 5 related questions to expand your understanding:

  1. What is the arithmetic mean of two other variables, aa and bb, if the sum of their arithmetic means equals 10?
  2. How would the solution change if the arithmetic mean given were a different number?
  3. Can you solve for xx if the arithmetic mean of 4 and 2x+72x + 7 is 6?
  4. What is the formula for the arithmetic mean of three numbers?
  5. 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