Collette and Jakara went shopping at a local music store. The shop advertised that all CDs marked with a red dot,r, were one price and all CDs marked with a green dot,g, were another price. Collette bought 2 green-dot CDs and 4 red-dot CDs for $52. Jakara bought 3 red-dot CDs and 1 green-dot CD for $34. Write and solve a system of equations to determine how much the store charges for each green-dot and each red-dot CD.

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absor201 absor201 · Answer 1 · 2019-12-07T17:01:42+01:00

The store charges $8 for one red dot CD and $10 for one green dot CD.

Step-by-step explanation:

Given,

Red dot CDs = r

Green dot CDs = g

According to given statement;

4r+2g=52 Eqn 1

3r+g=34 Eqn 2

Multiplying Eqn 2 by 2;

[tex]2(3r+g=34)\\6r+2g=68\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](6r+2g)-(4r+2g)=68-52\\6r+2g-4r-2g=16\\2r=16[/tex]

Dividing both sides by 2;

[tex]\frac{2r}{2}=\frac{16}{2}\\r=8[/tex]

Putting r=8 in Eqn 2

[tex]3(8)+g=34\\24+g=34\\g=34-24\\g=10[/tex]

The store charges $8 for one red dot CD and $10 for one green dot CD.

Keywords: linear equation, subtraction

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