Make the equation correct by swapping numbers — Which interchange of numbers makes the statement true? 8 × 20 ÷ 3 + 9 − 5 = 38

Introduction / Context:Interchange problems ask which pair of numbers, when swapped, turns a false arithmetic statement into a true one. You must respect operator precedence when reevaluating the expression after each hypothetical swap.

Given Data / Assumptions:

• Original expression: 8 × 20 ÷ 3 + 9 − 5.
• Goal value: 38.
• Allowed operation: swap exactly one of the given pairs of numbers in the options.

Concept / Approach:Compute the expression after each candidate swap, honoring ×/÷ precedence. We look for a combination that lands exactly at 38.

Step-by-Step Solution:Test (3, 5) swap ⇒ 8 × 20 ÷ 5 + 9 − 3.Evaluate: 8 × 20 = 160; 160 ÷ 5 = 32; 32 + 9 = 41; 41 − 3 = 38.Hence the swap (3, 5) makes the equation true.

Verification / Alternative check:Check a distractor quickly: swap (8, 9) ⇒ 9 × 20 ÷ 3 + 8 − 5 = 60 + 3 = 63, not 38.

Why Other Options Are Wrong:

• (3, 9): 8 × 20 ÷ 9 + 3 − 5 ≈ 11.78, not 38.
• (3, 8): 3 × 20 ÷ 8 + 9 − 5 = 7.5 + 9 − 5 = 11.5.
• (8, 9): evaluates to 63 as shown.
• 'None of these': a valid swap does exist.

Common Pitfalls:Applying operations strictly left-to-right without precedence or swapping a number but forgetting to apply it at both of its original positions if it appears multiple times (here, each appears once).

Final Answer:3, 5