Translating a mixed-fraction condition: The sum of one-half and one-fifth of a number exceeds one-third of that number by 7 1/3. What is the number?

Introduction / Context:
Convert words into an algebraic equation involving fractions, then solve for the unknown number. Mixed fractions should be converted to improper fractions to simplify arithmetic.

Given Data / Assumptions:

• (1/2 + 1/5)x − (1/3)x = 7 1/3.
• 7 1/3 = 22/3.

Concept / Approach:
Combine like terms on the left: (1/2 + 1/5 − 1/3)x. Compute the common denominator and simplify to get a single coefficient times x. Then isolate x.

Step-by-Step Solution:

Verification / Alternative check:
Check: (1/2 + 1/5) of 20 = (10 + 4) = 14; one-third of 20 = 20/3 ≈ 6.666…; difference 14 − 6.666… = 7.333… = 7 1/3, correct.

Why Other Options Are Wrong:

• 15, 18, 30: Do not satisfy the exact fractional relation; plugging them in fails the difference test.

Common Pitfalls:
Misconverting 7 1/3 to an improper fraction or adding fractions without a common denominator.

Final Answer: