Question

If 3/4 of x is 9, what is the value of x?

• A. 4
• B. 6 3/4
• C. 12
• D. 12 1/4
• E. 13 1/3

Hint:

To solve an equation of the form \((\frac{a}{b})x = c\), you can always find \(x\) by multiplying the other side by the reciprocal: \(x = c \times \frac{b}{a}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves setting up and solving a linear equation with a fraction. The phrase "3/4 of x" means we need to multiply 3/4 by x.
Step 2: Key Formula or Approach:
The statement can be written as the following equation:
\[ \frac{3}{4} \times x = 9 \] Our goal is to isolate the variable \(x\).
Step 3: Detailed Explanation:
To solve for \(x\), we need to undo the multiplication by 3/4. We can do this by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3.
\[ \left(\frac{4}{3}\right) \times \frac{3}{4}x = 9 \times \left(\frac{4}{3}\right) \] The fractions on the left side cancel out:
\[ x = \frac{9 \times 4}{3} \] \[ x = \frac{36}{3} \] \[ x = 12 \] Step 4: Final Answer:
The value of \(x\) is 12. This corresponds to option (C).