the dress store is having a sale where all merchandise is 1/4 off. a woman buys $42 of merchandise at the sales price. what would she have had to pay at the regular price.

so she paid 3/4 of the original.

solve (3/4)x = 42

To answer this question, we need to calculate the original (regular) price of the merchandise before the discount. Here's how we can do that:

Step 1: Determine the discount rate
The sale states that all merchandise is 1/4 off, which means there is a discount of 1/4 or 25%.

Step 2: Calculate the discounted price
We know that the woman bought $42 worth of merchandise at the sales price. Since it's 1/4 off, the sales price is 75% of the regular price.
Let's represent the regular price as 'x'. The sales price, after taking 1/4 off, is (100% - 25%) or 75% of the regular price. So, we can write the equation:
0.75x = $42

Step 3: Solve for x
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.75:
x = $42 / 0.75

Step 4: Calculate the regular price
Now, we can calculate the regular price by evaluating the expression on the right side of the equation:
x = $56

Therefore, the woman would have had to pay $56 at the regular price before the discount.