To calculate the single equivalent discount rate for a loyal customer who spent $100 on Black Friday, we need to consider the multiple discounts offered by Georges cleaning supplies. Let's break it down step-by-step:
1. Loyalty discount: Georges cleaning supplies offers a 20% discount to their loyal customers. This means that the loyal customer will receive a 20% reduction in the total price.
2. Purchase discount: If the customer spends more than $50, they are eligible for an additional 15% discount. In this case, the customer spent $100, so they qualify for this discount.
3. Black Friday special discount: On Black Friday, an extra 30% discount was offered. This discount is applied after the loyalty and purchase discounts.
Now, let's calculate the single equivalent discount rate:
1. Apply the loyalty discount: 20% of $100 is $20. Subtract $20 from the original price of $100, leaving $80.
2. Apply the purchase discount: The additional 15% discount is applied to $80. 15% of $80 is $12. Subtract $12 from $80, leaving $68.
3. Apply the Black Friday special discount: The extra 30% discount is applied to $68. 30% of $68 is $20.40. Subtract $20.40 from $68, leaving $47.60.
Finally, to find the single equivalent discount rate, we compare the final discounted price of $47.60 to the original price of $100:
$100 - $47.60 = $52.40
So, the single equivalent discount rate for the loyal customer who spent $100 on Black Friday is 52.40%.