Final answer:
To calculate the original price of the shoes before a 75% discount, divide the discounted price by 25%, resulting in $204. For a different problem, add 7.5% sales tax to the jacket's price by multiplying $85 by the tax rate, resulting in a total of $91.38 after adding the tax amount to the original price.
Step-by-step explanation:
To find the original price of shoes before a 75% discount if they cost $51 after the discount, we need to work backwards from the discounted price. Since a 75% discount means the consumer pays 25% (100% - 75%) of the original price, we can set up the equation: 0.25 × (original price) = $51. To solve for the original price, divide $51 by 0.25, which results in the original price being $204. Therefore, the shoes were $204 before the 75% discount.
In a similar problem, Emily bought a jacket for $85. To find the total cost including a 7.5% sales tax, first we calculate the sales tax by multiplying the price of the jacket by the tax rate: $85 × 0.075 = $6.375. The total cost is the original price of the jacket plus the sales tax, which is $85 + $6.375 = $91.375. After rounding to the nearest cent, the total cost of the jacket would be $91.38.