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1. Howard's CD House sells new CDs for $15 each and used CDs for $6 each. Bre'anna bought 51 CDs and spent a
total of $576 on the CDs. If n represents the number of new CDs, and u represents the number of used CDs, how
many of each type of CD did she buy?

Respuesta :

The numbers of new CDs is 30 and the old CDs is 21.

To solve this problem, we have to write a system of equations in which we would know the numbers of each types of CD she bought.

System of Equations

This is used to solve a series or complex of word problems in which we can represent in a mathematical statements;

  • Let n represents numbers of new CDs
  • Let u represents numbers of old CDs

The equations can be represented as

[tex]n + u = 51 ...equation(i)\\15n + 6u = 576 ... equation(ii)[/tex]

Let's take equation (i)

Making n the subject of formula

[tex]n + u = 51\\n = 51 - u...equation(iii)[/tex]

we can put equation (iii) into equation (ii)

[tex]15n + 6u =576\\n = 51 - u\\15(51 - u) + 6u = 576\\765-15u + 6u = 576\\collect like terms\\765-576=15u - 6u\\189=9u\\9u/9 = 189/9\\u = 21[/tex]

Let's put the value of u into equation (i)

[tex]n + u = 51\\u = 21\\n + 21 = 51\\n = 51 - 21\\n = 30[/tex]

From the calculations above, the numbers of new CDs is 30 and the old CDs is 21.

Learn more on system of equations here;

https://brainly.com/question/13729904

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