Chapter 11.CT, Problem 20CT

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# A shopkeeper buys a mixture of nuts; the almonds cost $4.75 a pound, and the walnuts cost$ 3.45 a pound. Her total purchase weighs 3   lb and costs \$ 11.91 . Use Cramer’s rule to determine how much of each nut she bought.

To determine

To find:

The amount of each nut she bought

Explanation

Approach:

If a system of 2 linear equations in the 2 variables x, y; is equivalent to the matrix equation DX=B, and if D0, then its solutions are

x=|Dx||D|, y=|Dy||D|.

Here, Dx and Dz are the matrices obtained by replacing the 1st and 2nd column of D by the n×1 matrix B respectively.

Calculation:

Assume that x and y are the amounts of almonds and walnuts she bought.

Then,

x+y=34.75x+3.45y=11.91

Using Cramer’s rule,

|D|=|114.753.45|=3.454.75=1.3

|Dx|=|3111

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