Question

Four peaches and 12 nectarines cost $2.28. At the same shop, two peaches and 14 nectarines cost $2.10. Using matrix methods, find the cost of each piece of fruit.

The cost for a peach is $ ___________________ (round to two decimal places)
and the cost of a nectarine is $ _____________ (round to two decimal places).

Answer 1

Explanation:

Let's represent the cost of one peach as "x" and the cost of one nectarine as "y". We can set up a system of equations using the given information:

4x + 12y = 2.28

2x + 14y = 2.10

We can write this system in matrix form as AX = B, where

A = |4 12|

|2 14|

X = |x|

|y|

B = |2.28|

|2.10|

To solve for X, we can use the formula X = A^(-1)B, where A^(-1) is the inverse of matrix A.

First, we need to find the inverse of matrix A:

|4 12| |7/30 -2/15|

|2 14| = |-1/30 2/15|

Now we can use the formula X = A^(-1)B:

|x| |7/30 -2/15||2.28| |0.24|

|y| = |-1/30 2/15||2.10| = |0.12|

Therefore, the cost for a peach is $0.24 (rounded to two decimal places) and the cost for a nectarine is $0.12 (rounded to two decimal places).