Final answer:
To find the original price of the snowboard, we first calculate the price before the 5% member discount and then the price before the 15% store discount. This results in an original price of $390.49.
Step-by-step explanation:
To determine the original price of the snowboard before the discounts, we need to work backwards from the final price after both discounts have been applied. First, we acknowledge that the final price is the result of applying a 15% store discount and an additional 5% member discount. To figure out the original price, we consider that the final price constitutes 85% (100% - 15%) of the price after the store discount and then 95% (100% - 5%) of the original price. Therefore, we are looking for a number that, after being reduced by 15% and then by an additional 5%, equals $315.32.
Starting with the 5% member discount, if $315.32 represents 95%, then the price before this discount (which is also after the 15% store discount) was $315.32 / 0.95. After that, to account for the 15% store discount, we divide the result by 0.85 because that price represented 85% of the original price. By calculating these two steps, we can find the original price of the snowboard.
Step 1: Calculate the price before the member discount: $315.32 / 0.95 = $331.916
Step 2: Calculate the original price before the store discount: $331.916 / 0.85 = $390.489
To the nearest cent, the original price of the snowboard is $390.49, which corresponds to option b.