Final answer:
To find out how many mints and candies Susanna bought, we can set up a system of equations based on the given information. However, after solving the system, it can be concluded that there is no specific number of mints and candies that would satisfy the given conditions.
Step-by-step explanation:
To find out how many mints and candies Susanna bought, we can set up a system of equations based on the given information. Let's define the number of pounds of mints as 'm' and the number of pounds of candies as 'c'.
From the given information, we know that the mints cost $3 per pound and the candies cost $4 per pound. Susanna spent a total of $27 for mints and candies, and she bought a total of 8 pounds. We can express this information as two equations:
3m + 4c = 27 ...(1)
m + c = 8 ...(2)
Now, let's solve this system of equations using any method you prefer, such as substitution or elimination.
One way to solve this system is by elimination. Multiply equation (2) by -3 to make the coefficients of 'm' in both equations cancel out:
-3(m + c) = -3(8)
-3m - 3c = -24 ...(3)
Now, add equation (1) and equation (3) together:
(3m + 4c) + (-3m - 3c) = 27 + (-24)
Combine like terms:
m + c = 3 ...(4)
Now, solve equation (4) for 'c':
c = 3 - m ...(5)
Substitute equation (5) into equation (2):
m + (3 - m) = 8
Combine like terms:
3 = 5
This equation is inconsistent, which means there is no solution that satisfies all the given conditions. Therefore, there is no specific number of mints and candies that Susanna bought that would satisfy the given information.