Question

A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.

Answer 1

First we need to write the equations for the given scenario. Using the equations, we can form a system of matrix for the situation.

Let the customer buys, x pounds of almonds, y pounds of cashews and z pounds of walnuts. Since he buys 12 pounds of mixed nuts, we can write:

$x+y+z=12$ 

Total cost of these mixed nuts was $118. So we can write:

$7x+10y+12z=118$

Customer buys 2 more pounds of walnut than cashews. So, we can write:

$z=y+2 \\ \\ -y+z=2$

Using these equations, we can set up the system of matrix as shown below in the image.

Answer 2

Answer:

Step-by-step explanation:

Let the customer buys, x pounds of almonds, y pounds of cashews and z pounds of walnuts. Since he buys 12 pounds of mixed nuts

Then since total weight he purchases is 12, we get

x+y+z = 12...i

Next is rate of each nut multiplied by pounds and added give the total cost.

Hence we have

7x+10y+12z=118 ... ii

A customer buys 2 more pounds of walnuts than cashews.

z=y+2 or

y-z=-2 ....iii

This can be written in matrix form as

Ax =B

$\left[\begin{array}{ccc}1&1&1\\7&10&12\\0&1&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \\= \left[\begin{array}{ccc}12\\118\\-2\end{array}\right]$