System of equations — The difference of two numbers is 8 and one-eighth (1/8) of their sum is 35. Determine the two numbers.

Introduction / Context:When given relationships for sum and difference, you can solve for two numbers directly using linear equations. Recognizing that “one-eighth of their sum is 35” gives the sum immediately is the key step here.

Given Data / Assumptions:

• Let the numbers be a and b with a > b.
• a - b = 8.
• (1/8) * (a + b) = 35 → a + b = 280.
• We seek ordered pair (b, a) or (a, b) as presented in options.

Concept / Approach:Use the standard transformations: a = (sum + difference)/2 and b = (sum - difference)/2. This avoids solving two equations separately and guarantees integer results when sum and difference share parity.

Step-by-Step Solution:From (1/8)(a + b) = 35, compute sum: a + b = 35 * 8 = 280.Given difference: a - b = 8.Compute a = (280 + 8)/2 = 288/2 = 144.Compute b = (280 - 8)/2 = 272/2 = 136.

Verification / Alternative check:Check: a - b = 144 - 136 = 8; (1/8)(a + b) = (1/8)(280) = 35. Both conditions are satisfied, confirming the pair 136 and 144.

Why Other Options Are Wrong:

• 132,140 / 128,136 / 124,132 / 140,148: These pairs do not simultaneously yield difference 8 and sum 280.

Common Pitfalls:Forgetting to multiply 35 by 8 to get the sum; swapping sum and difference in the formulas; arithmetic slips when halving the totals.

Final Answer:136, 144