The phrase “20% then another 10%” contains an order. The first percentage changes the price that becomes the base of the second percentage. Writing both remaining-price factors and both intermediate amounts prevents the common mistake of adding the rates.
First discount leaves $80
Twenty percent off means paying 80%, so the first stage is $100 × 80/100 = $80. The first saving is $20. This $80 result, not the original $100, is the base named by “then another 10%.”
Second discount leaves $72
The additional 10% means paying 90% of $80: $80 × 90/100 = $72. The second saving is $8, and total savings are $20 + $8 = $28. Multiplying the factors directly confirms $100 × 0.80 × 0.90 = $72.
Verify 28% effective savings
Compare the $28 total savings with the $100 original: 28 ÷ 100 × 100 = 28%. Adding 20% and 10% would claim $30 savings, but the second discount removed only $8. The stage breakdown explains the two-dollar difference without any hidden rule.