Final answer:
By setting up a system of linear equations using the quantities and prices of the fruit baskets, converting it to matrix form, and finding the inverse of the coefficient matrix, we can solve for the individual costs of mangos and kiwis.
Step-by-step explanation:
To solve the problem of finding the cost of each type of fruit using the information provided by the store, we can set up a system of linear equations based on the quantities and total costs of the fruit baskets.
- Let m be the cost of one mango and k be the cost of one kiwi.
- The first basket's equation is 2m + 3k = 9 (two mangos and three kiwis for $9.00).
- The second basket's equation is 5m + 2k = 14.25 (five mangos and two kiwis for $14.25).
We can write this system as a matrix:
[[2, 3], [5, 2]] represents the coefficients and [9, 14.25] represents the total costs.
To find the inverse matrix, we calculate the inverse of the coefficient matrix. Once we have the inverse, we can use it to solve the system by multiplying the inverse matrix by the column of total costs.
This will give us the individual costs of mangos and kiwis, which represent the values of m and k. The results tell us how much the store charges for each mango and each kiwi.