To find the undiscounted pre-sale price of each type of can, we can start by setting up equations based on the given information.
Let's say the undiscounted pre-sale price of each can of tomatoes is T dollars, and the undiscounted pre-sale price of each can of mushrooms is M dollars.
From the information about Stacey's purchase:
- Stacey used her 20% discount card, which means she paid 80% of the total price.
- She bought 7 cans of tomatoes and 15 cans of mushrooms for a total price of $10.64.
We can write the equation as:
7T + 15M = 10.64 -------- (1)
From the information about Brian's purchase:
- Brian got a 30% discount on his purchase, which means he paid 70% of the total price.
- He bought 17 cans of tomatoes and 5 cans of mushrooms for a total price of $7.21.
We can write the equation as:
17T + 5M = 7.21 --------- (2)
Now, we have a system of two equations (equation 1 and equation 2) with two variables (T and M). We can solve this system of equations to find the values of T and M.
To solve the system of equations, we can use any method such as substitution or elimination. Here, I'll use the elimination method.
Multiplying equation 1 by 17 and equation 2 by 7 to eliminate the T variable:
119T + 255M = 180.88 ---------(3)
119T + 35M = 50.47 ---------(4)
Subtracting equation 4 from equation 3 to eliminate the T variable:
(119T - 119T) + (255M - 35M) = (180.88 - 50.47)
220M = 130.41
Dividing both sides of the equation by 220:
M = 130.41 / 220
M = 0.592
Substituting the value of M back into equation 1 to solve for T:
7T + 15 * 0.592 = 10.64
7T + 8.88 = 10.64
7T = 10.64 - 8.88
7T = 1.76
T = 1.76 / 7
T = 0.251
Therefore, the undiscounted pre-sale price of each can of tomatoes is $0.251 and the undiscounted pre-sale price of each can of mushrooms is $0.592.