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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The regular price of a shirt at a store is $dollar sign 11.70$ . The sale price of the shirt is $80 percent sign$ less than the regular price, and the sale price is $30 percent sign$ greater than the store's cost for the shirt. What was the store’s cost, in dollars, for the shirt? (Disregard the $$$ sign when entering your answer. For example, if your answer is $dollar sign 4.97$ , enter $4.97$ )

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Explanation

The correct answer is $1.8$ . It’s given that the regular price of a shirt at a store is $dollar sign 11.70$ , and the sale price of the shirt is $80 percent sign$ less than the regular price. It follows that the sale price of the shirt is $$ 11.70 (1 - \frac{80}{100})$ , or $dollar sign 11.70 left parenthesis 1 minus 0.8 right parenthesis$ , which is equivalent to $dollar sign 2.34$ . It’s also given that the sale price of the shirt is $30 percent sign$ greater than the store’s cost for the shirt. Let $x$ represent the store’s cost for the shirt. It follows that $2.34 = (1 + \frac{30}{100}) x$ , or $2.34 equals 1.3 x$ . Dividing both sides of this equation by $1.3$ yields $x equals 1.80$ . Therefore, the store’s cost, in dollars, for the shirt is $1.80$ . Note that 1.8 and 9/5 are examples of ways to enter a correct answer.