Question

If \(x\) increased by 50 percent is equal to 20, then \(x=\)

• A. \( \frac{40}{3} \)
• B. 10
• C. \( \frac{20}{3} \)
• D. 5
• E. \( \frac{3}{4} \)

Hint:

An increase of P percent on a number x is equivalent to multiplying x by (1 + P/100). A 50% increase is multiplying by 1.5. A 20% increase is multiplying by 1.2, etc. This is often faster than calculating the increase and adding it on.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires translating a statement about a percentage increase into a mathematical equation and then solving for the unknown variable \(x\).
Step 2: Key Formula or Approach:
"\(x\) increased by 50 percent" can be written mathematically as \(x + 0.50x\), which simplifies to \(1.5x\). We set this expression equal to 20 and solve for \(x\).
Step 3: Detailed Explanation:
The statement is: "\(x\) increased by 50 percent is equal to 20."
Let's write this as an equation: \[ x + (50% \text{ of } x) = 20 \] Convert the percentage to a decimal: 50% = 0.5. \[ x + 0.5x = 20 \] Combine the terms with \(x\): \[ 1.5x = 20 \] To solve for \(x\), it's easier to work with fractions. Convert 1.5 to a fraction: \(1.5 = \frac{3}{2}\). \[ \frac{3}{2}x = 20 \] To isolate \(x\), multiply both sides by the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \). \[ \left(\frac{2}{3}\right) \times \frac{3}{2}x = 20 \times \left(\frac{2}{3}\right) \] \[ x = \frac{40}{3} \] Step 4: Final Answer:
The value of \(x\) is \( \frac{40}{3} \).