Birchwood Outfitters Daily Jacket Sales
On one day, Birchwood Outfitters sold 18 Premium Down jackets and 22 Lightweight Canvas jackets, taking in a total of $3,440 in revenue. The price of a Lightweight Canvas jacket is $40 less than the price of a Premium Down jacket.
What is the price, in dollars, of one Lightweight Canvas jacket?
A linear equation fits a sales problem when two prices differ by a fixed amount and their combined revenue is given. Let the requested price be the unknown, write the other price using the difference, then multiply each price by its own quantity before adding. Enter the finished equation as a Desmos regression; the main trap is giving both kinds the same price.
Hints
- Hint 1
The Lightweight Canvas jacket is less expensive, so let its price be dollars. To write the Premium Down price, do you add or subtract the stated difference?
- Hint 2
Each kind’s revenue is the number of jackets sold times the price of one jacket. Use the Premium Down price with the Premium Down count, then add the Lightweight Canvas revenue to reach the daily total.
Step-by-step
Build one revenue equation
Step 1Write both prices with one unknown
Let be the price, in dollars, of one Lightweight Canvas jacket. It costs $40 less than a Premium Down jacket, so the higher Premium Down price is , not .
- Step 2
Match each price to its jacket count
The Premium Down jackets bring in dollars, and the Lightweight Canvas jackets bring in dollars. Multiply each kind’s count by that kind’s price. Their revenue, or money from sales, totals , so:
- Step 3
Solve for the requested price
Type in Desmos. Use for the unknown price instead of the graphing variable ; tells Desmos to find the value that makes the two sides equal. Under PARAMETERS, it reports . Since is the Lightweight Canvas price, one jacket costs $68. Choice B.