ACT Math · Ratios, rates, and percents

An item originally priced at $120 is discounted 25%, and then an additional 10% is taken off the new price. What is the final price?

An item originally priced at $120 is discounted 25%, and then an additional 10% is taken off the new price. What is the final price?

Answer and explanation

Answer: G: $81.00

Apply the discounts one at a time. A 25%25\% discount leaves 75%75\% of the price: 120(0.75)=90120(0.75)=90. Then 10%10\% off the new price leaves 90%90\%: 90(0.90)=8190(0.90)=81 dollars, choice G. Choice F ($78) treats the discounts as a single combined 35%35\% off, 120(0.65)120(0.65), but the second discount applies to a smaller amount. Choice J ($102) subtracts only 15%15\%, which is the difference between the two rates rather than a combination of them. Choice H ($90) applies only the first discount. Successive percent changes multiply: 0.75⋅0.90=0.6750.75\cdot0.90=0.675.

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