   Chapter 11.CR, Problem 73E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# Investments: Clarisse invests $60 , 000 in money-market accounts at three different banks. Bank A pays 2 % interest per year, bank B pays 2.5 % , and bank C pays 3 % . She decides to invest twice as much in Bank B as in the other two banks. After 1 year, Clarisse has earned$ 1575 in interest. How much did she invest in each bank?

To determine

To find:

The amount of money Clarisse invested in bank A, B, and C.

Explanation

Given:

Clarrise has a total sum of $60,000 from which she invested twice as much in Bank B as in Bank A and Bank C. After one year, she earned a total interest of$1575.

Approach:

The solution of the linear system will be obtained by putting the augmented matrix of the linear system into its reduced row-echelon form.

Calculation:

Let, Clarisse invest $x,$y, and \$z in bank A, B, and C, respectively.

According to the given information, we get the following equations.

x+y+z=60,000

y=2(x+z)2xy+2z=0

x(2100)+y(2.5100)+z(3100)=1575x50+y40+3z100=1575

Considering this linear system, the augmented matrix is .

Transform the augmented matrix into row echelon form.

Perform the transformation R2R22R1.

[1116000022(1)12(1)22(1)02(60000)15014031001575]

Perform the transformation R3R3R150.



Perform the transformation R2R23.

[111600000(13)3(13)0(13)120000(13)012001100375]

Perform the transformation R3R31200R2

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