Three-number relation with sum repair (clarified): The first number is twice the second and also three times the third. The sum of the three numbers is 154. What is the difference between the first and the third number?

Introduction / Context:
(Recovery-first clarification) The original stem was ambiguous. To make it solvable without altering the core intent, we clarify the standard setup: the first number relates to the second and third by simple multiples, and the total sum is 154. We are asked for the difference between the first and third numbers.

Given Data / Assumptions:

• Let the three numbers be F (first), S (second), T (third).
• Relations: F = 2S and F = 3T.
• Sum: F + S + T = 154.

Concept / Approach:
Use the relations to express S and T in terms of F, then compute the sum to solve for F. Once F is known, recover T and compute F − T. This linear system approach is direct and avoids unnecessary complexity.

Step-by-Step Solution:
From F = 2S ⇒ S = F/2. From F = 3T ⇒ T = F/3.Sum: F + F/2 + F/3 = 154.Combine fractions: F*(1 + 1/2 + 1/3) = F*(11/6) = 154.Solve for F: F = 154 * 6 / 11 = 84.Then T = F/3 = 28. Difference: F − T = 84 − 28 = 56.

Verification / Alternative check:
Compute S = F/2 = 42. Check sum: 84 + 42 + 28 = 154. All conditions are satisfied.

Why Other Options Are Wrong:
42, 62, 68, and 74 do not equal F − T under the validated relations and sum.

Common Pitfalls:
Reversing the multipliers; forgetting to include all three terms in the sum; arithmetic slips when handling fractions 1/2 and 1/3.

Final Answer:
56