Stacey used her 20% discount card to buy 7 cans of tomatoes and 15 cans of mushrooms for $10.64. The next day Brian spent $ 7.21 on 17 cans of tomatoes and 5 cans of mushrooms in a "30% off" sale. Find the undiscounted pre- sale price of each type of can.

let's use T for tomato and M for mushroom,Stacey:$10.64 is 80% of the original price of 7T and 15M so 20% discount will equal to 2.66 and the original price will be 13.3.

Brian:7.21 is 70% of the original price of 17T and 5M so 30% will equal to 3.09 and the original price will be 10.3.
Stacey:7T+15M=13.3
Brian:17T+5M=10.3
now multiply Brian by 5 will get
7T+15M=13.3
51T+15M=30.9
now subtract it will get
44T=17.6 and T=$.40 and M=$.70

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.