Stephanie has $67 to spend at a store. The store currently has a sale where the sale price is 23% off the marked price. What is the highest marked price that Stephanie can afford? (Round to the nearest cent, or hundredth of a dollar.)
can you please show it step by step?
sale price is 77% of marked price, so
marked = sale/.77
she has $67, so
marked = 67/.77 = $87.01
Sure! Here's how you can calculate the highest marked price that Stephanie can afford step by step:
Step 1: Convert the percentage discount to a decimal. The discount is 23%, so we write it as 0.23.
Step 2: Calculate the amount of discount by multiplying the original price by the discount rate. In this case, the discount is 23% off, so the amount of discount is 0.23 * original price.
Step 3: Calculate the sale price by subtracting the amount of discount from the original price. The sale price is the amount Stephanie will pay after the discount, so we subtract the discount from the original price: original price - (0.23 * original price).
Step 4: Set up an equation to solve for the highest marked price. We want to find the highest marked price that Stephanie can afford, so we set up the equation: original price - (0.23 * original price) = $67.
Step 5: Solve the equation for the original price. Add the amount of discount (0.23 * original price) to both sides of the equation to isolate the original price: original price = $67 + (0.23 * original price).
Step 6: Simplify the equation by combining like terms. Move the (0.23 * original price) term to the other side of the equation: original price - 0.23 * original price = $67.
Step 7: Factor out the original price from the left side of the equation: original price * (1 - 0.23) = $67.
Step 8: Simplify the equation further by evaluating the expression (1 - 0.23) = 0.77: original price * 0.77 = $67.
Step 9: Solve the equation for the original price by dividing both sides of the equation by 0.77: original price = $67 / 0.77.
Step 10: Use a calculator to divide $67 by 0.77 to find the original price: original price ≈ $87.01.
Therefore, the highest marked price that Stephanie can afford is approximately $87.01, rounding to the nearest cent.