ACT Math · Ratios, rates, and percents

An item originally priced at $200 is discounted three separate times, each time by 10% off the current price. What is the final price?

An item originally priced at $200 is discounted three separate times, each time by 10% off the current price. What is the final price?

Answer and explanation

Answer: B: $145.80

Each discount takes 10%10\% off the current price, so multiply by 0.90.9 three times: 200(0.9)=180200(0.9)=180, then 180(0.9)=162180(0.9)=162, then 162(0.9)=145.80162(0.9)=145.80. The final price is $145.80, choice B. Equivalently, 200(0.9)3=200(0.729)=145.80200(0.9)^3=200(0.729)=145.80. Choice A ($140) treats the three discounts as a single 30%30\% discount, which ignores that each discount is on a smaller amount. Choice D ($162) applies only two discounts. Choice C ($150) is a rough guess. Successive percent discounts are multiplied, not added.

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