A retail store lists a jacket for $290, less 18%. A department store lists the same jacket for $265, less 12%. a) Which store is offering the item for a cheaper price, and by how much? b) What additional trade discount rate must the store with the higher price provide to match the lower price?

To determine which store offers the jacket for a cheaper price and by how much, let's calculate the final price after the discounts for both stores.
a) Comparison of Final Prices:

Retail Store:

List Price: $290
Discount: 18%
Amount of Discount: $290 \times 0.18 = $52.20
Final Price: $290 - $52.20 = $237.80


Department Store:

List Price: $265
Discount: 12%
Amount of Discount: $265 \times 0.12 = $31.80
Final Price: $265 - $31.80 = $233.20



Comparing both final prices, the department store offers the jacket for cheaper at $233.20.
Difference in Price:

The difference in price: $237.80 - $233.20 = $4.60

So, the department store offers the jacket for $4.60 less than the retail store.
b) Additional Trade Discount Rate Required:
To find the additional discount needed at the retail store to match the department store's price:

Current Final Price at Retail Store: $237.80

Desired Final Price: $233.20 (price at the department store)

Difference to Match: $237.80 - $233.20 = $4.60


Let's calculate the additional discount rate that would reduce the retail store's price by $4.60:

Let x be the additional discount rate.

290 × x = 4.60
x = 290 4.60 ​ ≈ 0.01586 or 1.586%
Hence, the retail store would need to provide an additional discount of approximately 1.59% to match the department store's price.

Answered by SophiaElizab | 2025-07-21