Question

For exercises 17 and 18, use this scenario: A retired woman has $\$ 50,000$ to invest but needs to make $\$ 6,000$ a year from the interest to meet certain living expenses. One bond investment pays 15$\%$ annual interest. The rest of it she wants to put in a CD that pays 7$\% .$ If we let $x$ be the amount the woman invests in the 15$\%$ bond, how much will she be able to invest in the CD?

Name: Problem 17, Chapter 2: College Algebra
Uploaded: 2020-03-19T00:34:39-08:00
Duration: 1 min 7 s
Channel: Vicki Stebbins
Description: For exercises 17 and 18, use this scenario: A retired woman has 50,000 to invest but needs to make 6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7% . If we let x be the amount the woman invests in the 15% bond, how much will she be able to invest in the CD?

   For exercises 17 and 18, use this scenario: A retired woman has $\$ 50,000$ to invest but needs to make $\$ 6,000$ a year from the interest to meet certain living expenses. One bond investment pays 15$\%$ annual interest. The rest of it she wants to put in a CD that pays 7$\% .$

If we let $x$ be the amount the woman invests in the 15$\%$ bond, how much will she be able to invest in the CD?

College Algebra

Jay Abramson 1st Edition

Chapter 2, Problem 17

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Solved by Expert Vicki Stebbins

03/19/2020

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For exercises 17 and 18, use this scenario: A retired woman has $\$ 50,000$ to invest but needs to make $\$ 6,000$ a year from the interest to meet certain living expenses. One bond investment pays 15$\%$ annual interest. The rest of it she wants to put in a CD that pays 7$\% .$ If we let $x$ be the amount the woman invests in the 15$\%$ bond, how much will she be able to invest in the CD?

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Key Concepts

Defining Variables

In algebraic word problems, it is essential to assign variables to represent unknown quantities. This practice simplifies the translation of the problem’s information into a mathematical format and allows for the systematic development of equations to solve for these unknowns.

Algebraic Expression Setup

Setting up algebraic expressions involves translating the relationships and constraints given in the problem into mathematical statements. This skill includes expressing one unknown quantity in terms of another based on total sums or differences, which is crucial for solving mixture and allocation problems.

Financial Interest Calculations

Understanding financial interest calculations is key when dealing with investment scenarios. This concept involves applying known interest rates to different amounts of money, which helps in formulating equations that relate the invested amounts to the expected returns.

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