14. higher order thinking antwan went to the store to buy a sweater that was on sale for 40% off the…

14. higher order thinking antwan went to the store to buy a sweater that was on sale for 40% off the original price. it was then put on clearance at an additional 25% off the sale price. he also used a coupon that saved him an additional $5. antwan did not spend more than $7.60 for the sweater. what are the possible values for the original price of the sweater?

14. higher order thinking antwan went to the store to buy a sweater that was on sale for 40% off the original price. it was then put on clearance at an additional 25% off the sale price. he also used a coupon that saved him an additional $5. antwan did not spend more than $7.60 for the sweater. what are the possible values for the original price of the sweater?

Answer

Explanation:

Step1: Let the original price be (x).

The price after (40%) off is (x(1 - 40%)=0.6x).

Step2: Find the price after additional (25%) off.

The price after an additional (25%) off the sale - price is (0.6x(1 - 25%)=0.6x\times0.75 = 0.45x).

Step3: Consider the coupon.

After using the ($5) - off coupon, the final price is (0.45x-5).

Step4: Set up the inequality.

Since Antwan did not spend more than ($7.60), we have the inequality (0.45x-5\leqslant7.60).

Step5: Solve the inequality.

Add (5) to both sides: (0.45x\leqslant7.60 + 5), so (0.45x\leqslant12.6). Divide both sides by (0.45): (x\leqslant\frac{12.6}{0.45}). Calculate (\frac{12.6}{0.45}=\frac{1260}{45}=28).

Answer:

The original price (x) of the sweater satisfies (x\leqslant28), so the possible values of the original price are all real numbers (x) such that (0\lt x\leqslant28) (assuming the price (x>0)).