A pair of shoes costs $180. Shop A applies a 20% discount first, then charges 9% GST on the discounted price. Shop B charges 9% GST first, then applies a 20% discount on the GST-inclusive price. How much cheaper is Shop A than Shop B?
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Worked Solution
Step 1 (Shop A): Discount first: $180 × 0.80 = $144. Then GST: $144 × 1.09 = $156.96.
Step 2 (Shop B): GST first: $180 × 1.09 = $196.20. Then discount: $196.20 × 0.80 = $156.96.
Step 3: Difference = $156.96 − $156.96 = $0.
Math insight: Multiplication is commutative. $180 × 0.80 × 1.09 = $180 × 1.09 × 0.80 — the order of multiplication does not change the product.
Correct answer: $0
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