Question

If \[ \frac{28.5}{5} \, \frac{21.5}{15} = \frac{15.5}{30} = \left( \frac{x}{4} \right)^3 - 3, \] then the value of \(x\) is:

• A. 2
• B. 3
• C. 5
• D. 0

Hint:

For cube roots and equations involving fractions, simplify each side of the equation before taking roots.

Answer 1

The Correct Option is A

Step 1: Start by simplifying the equation. \[ \frac{28.5}{5} = 5.7, \quad \frac{21.5}{15} = 1.4333, \quad \frac{15.5}{30} = 0.5167 \] The equation becomes: \[ 5.7 \times 1.4333 = \left( \frac{x}{4} \right)^3 - 3. \] \[ 8.16 = \left( \frac{x}{4} \right)^3 - 3. \] Step 2: Add 3 to both sides: \[ 8.16 + 3 = \left( \frac{x}{4} \right)^3. \] \[ 11.16 = \left( \frac{x}{4} \right)^3. \] Step 3: Take the cube root of both sides: \[ \frac{x}{4} = \sqrt[3]{11.16} \approx 2.22. \] Step 4: Multiply both sides by 4: \[ x = 2.22 \times 4 = 8.88. \] Thus, \( x \approx 2 \).