If $8\frac{1}{3}\%$ of $x=150$, then the value of x in:

Question

Accepted Answer

The correct option is 2:
To solve this problem, we need to understand how to convert a mixed percentage to a fraction and then solve a linear equation.

Step 1: Convert the mixed percentage to an improper fraction.
The given percentage is $8\frac{1}{3}%$.
First, convert the mixed number $8\frac{1}{3}$ to an improper fraction:
$8\frac{1}{3} = \frac{(8 \times 3) + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}$

Step 2: Convert the percentage to a fraction.
To convert a percentage to a fraction, divide by 100.
$8\frac{1}{3}% = \frac{25}{3}% = \frac{25}{3 \times 100} = \frac{25}{300}$

Step 3: Simplify the fraction.
$\frac{25}{300} = \frac{1}{12}$ (by dividing both numerator and denominator by 25)

Step 4: Set up the equation.
The problem states that $8\frac{1}{3}%$ of $x = 150$.
Using the fractional equivalent, we can write this as:
$\frac{1}{12} \times x = 150$

Step 5: Solve for $x$.
To find the value of $x$, multiply both sides of the equation by 12:
$x = 150 \times 12$
$x = 1800$

Thus, the value of $x$ is 1800.

The incorrect option is 1: This option (1700) might arise from calculation errors during the conversion of the percentage or in the final multiplication.
The incorrect option is 3: This option (1500) might arise from incorrect conversion of the percentage to a fraction or a calculation error. For instance, if one mistakenly thought $10%$ of $x = 150$, then $x = 1500$.
The incorrect option is 4: Since we found a specific value for $x$, this option is incorrect.