For a friend's birthday party, Shiloh and Leah bought a handbag each. Shiloh bought the handbag at $1584 after a 12% discount. If Leah bought the same handbag at $1656, what was the percentage discount given to Leah?
Question
For a friend's birthday party, Shiloh and Leah bought a handbag each. Shiloh bought the handbag at 1656, what was the percentage discount given to Leah?
Solution
Sure, here's how you can solve this problem:
Step 1: First, we need to find the original price of the handbag. Since Shiloh bought the handbag at $1584 after a 12% discount, we can set up the equation 1584 = 0.88x (because 100% - 12% = 88%, and we convert this percentage to a decimal by dividing by 100). Solving for x gives us the original price of the handbag.
Step 2: Solve the equation 1584 = 0.88x to find x. You can do this by dividing both sides of the equation by 0.88. This gives you x = 1584 / 0.88 = $1800.
Step 3: Now that we know the original price of the handbag is 1656, so the amount of the discount is 1800 - 1656 = $144.
Step 4: To find the percentage discount, we divide the amount of the discount by the original price and multiply by 100. So, the percentage discount for Leah is (144 / 1800) * 100 = 8%.
So, Leah was given an 8% discount.
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