A store lists suits with a regular price of $192. The sale price is 7/8 of the regular price, and later the price is changed to 11/12 of the sale price. What is the final price?

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Multiple Choice

A store lists suits with a regular price of $192. The sale price is 7/8 of the regular price, and later the price is changed to 11/12 of the sale price. What is the final price?

Explanation:
Understanding how sequential percentage changes work helps here. Prices that are reduced by a fraction are multiplied by that fraction. Start with the regular price: 192. The sale price is 7/8 of that, so you get 192 × 7/8 = 168. Now the price changes to 11/12 of the sale price, so the final price is 168 × 11/12 = 154. You could also multiply all at once: 192 × (7/8) × (11/12) = 192 × 77/96 = 154. The final price must be less than the sale price, so it should be below 168. 154 fits, while 168 is the sale price itself, and 176 or 180 would exceed the sale price, which isn’t possible after applying both reductions.

Understanding how sequential percentage changes work helps here. Prices that are reduced by a fraction are multiplied by that fraction.

Start with the regular price: 192. The sale price is 7/8 of that, so you get 192 × 7/8 = 168. Now the price changes to 11/12 of the sale price, so the final price is 168 × 11/12 = 154. You could also multiply all at once: 192 × (7/8) × (11/12) = 192 × 77/96 = 154.

The final price must be less than the sale price, so it should be below 168. 154 fits, while 168 is the sale price itself, and 176 or 180 would exceed the sale price, which isn’t possible after applying both reductions.

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