To define the functions for the discounts, we can represent the two types of discounts as follows:
-
Function f(x) - This function represents the dollars off given by the coupon.
- Let \( f(x) = 5 \) (this means you get $5 off regardless of the initial price).
-
Function g(x) - This function represents the percentage off the jeans.
- For a pair of jeans that costs \( x \) dollars, the function can be defined as: \[ g(x) = 0.25 \times x \] This means that you get 25% off the price \( x \).
Now, let's find the final price of the jeans using both types of discounts for a pair of jeans that costs $40.
Option 1: Using the dollar off coupon first (f(x) first)
-
Apply f(x):
- Start with the full price: \( 40 \)
- Apply the coupon: \[ P_1 = 40 - f(40) = 40 - 5 = 35 \]
-
Then apply g(x):
- Apply the 25% discount on the new price: \[ g(35) = 0.25 \times 35 = 8.75 \]
- The final price after both discounts: \[ P_1' = 35 - g(35) = 35 - 8.75 = 26.25 \]
Option 2: Applying the percentage discount first (g(x) first)
-
Apply g(x):
- Calculate 25% off the original price: \[ g(40) = 0.25 \times 40 = 10 \]
- The new price after the 25% discount: \[ P_2 = 40 - g(40) = 40 - 10 = 30 \]
-
Then apply f(x):
- Now apply the $5 off coupon on the reduced price: \[ P_2' = 30 - f(30) = 30 - 5 = 25 \]
Conclusion
Now we compare the final prices from both options:
- Option 1 gave a final price of $26.25.
- Option 2 gave a final price of $25.00.
The best price for the pair of jeans is thus $25.00, obtained by applying the 25% discount first followed by the $5 off coupon.