Two stores carry a similar stereo for the same original price of $573. One store offers a 16% discount and the second sells the stereo for $458.40. Which store gives the bigger percent discount? Justify your answer.
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To determine which store offers the bigger percent discount, we need to compare the discount amount from each store.
Let's start by calculating the discount amount from the first store:
Original price: $573
Discount rate: 16%
To find the discount amount, we need to calculate 16% of $573. We can do this by multiplying the original price by the decimal representation of the discount rate:
Discount amount = $573 * 0.16
Discount amount = $91.68
Therefore, the first store offers a discount of $91.68.
Now let's consider the second store's offer:
Selling price: $458.40
To calculate the discount amount from the second store, we need to find the difference between the original price and the selling price:
Discount amount = $573 - $458.40
Discount amount = $114.60
Therefore, the second store offers a discount of $114.60.
Now we can compare the discount amounts to determine which store offers a bigger percent discount. Since the discount amount from the second store is larger ($114.60) compared to the first store's discount amount ($91.68), we can conclude that the second store gives a bigger percent discount.
To further verify this, we can calculate the percent discount for both stores:
For the first store:
Percent discount = (Discount amount / Original price) * 100
Percent discount = ($91.68 / $573) * 100
Percent discount ≈ 16%
For the second store:
Percent discount = (Discount amount / Original price) * 100
Percent discount = ($114.60 / $573) * 100
Percent discount ≈ 20%
As we can see, the second store offers a larger percent discount (approximately 20%) compared to the first store's discount (approximately 16%). Therefore, the second store gives the bigger percent discount.