Question

If the sum of one-half and one-fifth of a number exceeds one-third of that number by 7¹⁄₃, then the number is:

• A. 17
• B. 20
• C. 25
• D. 32

Hint:

When dealing with fractions of a "number," assume the number is $x$ and clear the denominators early by multiplying the entire equation by the LCM.

Answer 1

The Correct Option is B

Concept: Translate the word problem into a linear algebraic equation.

Step 1: Set up the equation.
Let the number be $x$.
The equation is: $(\frac{1}{2}x + \frac{1}{5}x) - \frac{1}{3}x = 7\frac{1}{3}$
Convert $7\frac{1}{3}$ to an improper fraction: $\frac{22}{3}$.

Step 2: Find a common denominator.
The LCM of 2, 5, and 3 is 30.
$\frac{15x + 6x - 10x}{30} = \frac{22}{3}$
$\frac{11x}{30} = \frac{22}{3}$

Step 3: Solve for $x$.
$11x = \frac{22 \times 30}{3} = 22 \times 10 = 220$
$x = 220 \div 11 = 20$.