cost of cd

by Mackenzie

Andrew had $93.00. With this money, he could buy 3 CDs and 4 books. However, he bought only 2 CDs and 3 books and had $27.00 left. What was the cost of each CD?


Solution


This problem will lead to a system of linear equations



Let x be the cost of 1 cd



Let y be the cost of 1 book



Cost of 3 CDs + cost of 4 books must equal to 93 dollars.



3 × x + 4 × y = 93



3x + 4y = 93



When he bought 2 CDs and 3 books he had 27 dollars left.



The statement above means that



Cost of 2 CDs + cost of 3 books = 93 - 27



Cost of 2 CDs + cost of 3 books = 66



2x + 3y = 66



You now have a system of equations to solve



3x + 4y = 93 equation 1



2x + 3y = 66 equation 2



Multiply equation 1 by -2 and equation 2 by 3



We get



-6x + -8y = -186 equation 3


6x + 9y = 198 equation 4



Add the left sides and right sides of equation 3 and equation 4.



-6x + 6x + -8y + 9y = -186 + 198



0 + -8y + 9y = -186 + 198



-8y + 9y = -186 + 198



y = -186 + 198



y = 12


Use equation 2 to find y



2x + 3y = 66



2x + 3 × 12 = 66




2x + 36 = 66



2x + 36 - 36 = 66 - 36



2x = 66 - 36



2x = 30



Divide both sides by 2



2x / 2 = 30 / 2



x = 15






Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to System of linear equations.





Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz