20% off, then 10% off a $100 basket
- First saving = $20; new subtotal = $80.
- Second saving = 10% of $80 = $8; pay $72.
- Overall saving = $28 out of $100 = 28%.
Successive coupons & percent of a percent
Every new coupon acts on the amount eligible at that step.
Keep the new total after every step
A 20% discount leaves 80% of a price. A subsequent 10% discount leaves 90% of that remaining amount. Together they leave 0.80 × 0.90 = 0.72 of the original, so the total discount is 28%. The second coupon saves less money because its base is smaller.
Does coupon order matter?
Predict first. Change one value, then explain what stays the same and what changes. All bars use the same scale within a model.
Order can matter for mixed coupons
Two unrestricted percentage discounts on the same total give the same unrounded result in either order because multiplication commutes. A fixed-dollar coupon and a percentage coupon generally give different totals when reordered. Eligibility, caps, minimum spends and step-by-step rounding can also change what happens.
Optimize without losing the evidence
For Extreme Couponing, list the subtotal before each coupon, its eligible base, the saving and the new subtotal. Compare strategies using the same original basket and rules. Calculate overall savings as (original − final) ÷ original × 100%, comparing both prices on the same tax basis. Never add successive discount percentages as if they shared a base.
Worked examples
Reorder $20 off and 25% off a $100 basket
- $20 off first: (100 − 20) × 0.75 = $60.
- 25% off first: 100 × 0.75 − 20 = $55.
- The second order saves $5 more, assuming both coupons are allowed.
Guided Practice
A $120 basket has $50 off then 20% off. Compare the reverse order.
A first hint
Write the intermediate subtotal before each percentage.
Compare your reasoning
Dollar first: (120 − 50) × 0.80 = $56. Percent first: 120 × 0.80 − 50 = $46. Reordering saves another $10 under these unrestricted rules.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Connections
Find 20% of 30% of 200. Explain why it is 6% of 200, then connect that reasoning to a coupon applied after a previous discount.
Use it in Extreme Couponing
Record the whole, the percent multiplier and the result with units. For each coupon, use the eligible amount at that step. State whether a resale percentage means percent of cost or markup on cost.