end of season sale for summer clothes advertises 30% to 45% off the original price. What was the highest original price of a swimsuit that is now on sale for $12.99? What was the lowest original price?
0.7x = 12.99
x = $18.56
0.55x = 12.99
x = $23.62
To find the highest and lowest original prices for the swimsuits, we need to work with the given discount range (30% to 45% off) and the sale price ($12.99).
Let's begin with the highest original price. If we assume that the swimsuit was originally priced at "x" dollars, and it is now on sale for $12.99, we can set up the equation as follows:
x - (30/100) * x = $12.99
Simplifying the equation, we get:
(1 - 30/100) * x = $12.99
(70/100) * x = $12.99
Now, we can solve for "x" by dividing both sides of the equation by (70/100):
x = $12.99 / (70/100)
x = $12.99 * (100/70)
x ≈ $18.56
Therefore, the highest original price for a swimsuit that is now on sale for $12.99 is approximately $18.56.
Now, let's calculate the lowest original price. Following the same approach, we can set up the equation as:
x - (45/100) * x = $12.99
(1 - 45/100) * x = $12.99
(55/100) * x = $12.99
Solving for "x" by dividing both sides by (55/100), we get:
x = $12.99 / (55/100)
x = $12.99 * (100/55)
x ≈ $23.62
Thus, the lowest original price for a swimsuit that is now on sale for $12.99 is approximately $23.62.