118 dollars in pounds

Asked by maham237 @ 03/01/2021 in Mathematics viewed by 454 People

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.

Answered by maham237 @ 03/01/2021

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.

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118 dollars in pounds

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