PLEASE SHOW YOUR WORK.. Marty paid $72 for a jacket that had been marked down 20%. Create a linear model to represent this and use it to calculate the original price of the jacket.
(1 - .2)x = 72
Solve for x.
To solve this problem using a linear model, we can start by representing the original price of the jacket as x.
We know that Marty paid $72, which is the reduced price after a 20% discount. To calculate the discounted price, we subtract the discount amount from the original price:
Discounted price = Original price - Discount amount
The discount amount is calculated by multiplying the original price by the discount rate (expressed as a decimal). In this case, the discount rate is 20% or 0.20:
Discount amount = Original price * Discount rate
Substituting the variables, we can rewrite this equation as:
72 = x - (x * 0.20)
Now, we can simplify the equation:
72 = x - 0.20x
To solve for x, we can combine the like terms:
72 = 0.80x
Next, we isolate x by dividing both sides of the equation by 0.80:
72 / 0.80 = x
Using a calculator, we divide 72 by 0.80, which gives us:
90 = x
Therefore, the original price of the jacket was $90.
In summary, the linear model for this problem is:
Original price = Discounted price + (Discount amount)
x = 72 + (x * 0.20)
After simplifying the equation, we find that the original price of the jacket was $90.
To create a linear model to represent this situation, we can use the formula for calculating a discount amount:
Discount = Original Price * Discount Rate
We are given that the discount is 20% and the final discounted price is $72. Let's assume the original price is represented by "x."
So, the equation can be written as:
Discount = x * 0.20
We know that the final discounted price is $72, so the equation can be written as:
$72 = x - (x * 0.20)
Simplifying the equation:
$72 = x - 0.20x
Combining like terms:
$72 = 0.80x
To find the original price (x), we can solve for x:
x = $72 / 0.80
x ≈ $90
Therefore, the original price of the jacket was approximately $90.