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On sports day at Lakewood middle school, gold, silver, and bronze medals were awarded to the top three finishers in each event Miniature replicas of the medals were sold as souvenirs in booths around the field. For $26, attendees could purchase a package containing 5 gold, 4 silver, and 2 bronze replicas, or one containing 4 gold, 4 silver, and 4 bronze replicas, or one that had 3 gold, 4 silver, and 6 bronze replicas. Which system of equations may be used to find the price, in dollars, of each type of replica?

Respuesta :

MrRoyal

Answer:

[tex]5G + 4S + 2B = 26[/tex]

[tex]2G + 2S + 2B = 13[/tex]

[tex]3G + 4S + 6B = 26[/tex]

Step-by-step explanation:

Given

Represent Gold with G, Silver with S and Bronze with B

Required

Determine the system of equations

The packages are represented as:

The first: 5G + 4S + 2B

The second: 4G + 4S + 4B

The third: 3G + 4S + 6B

Each of the package costs $26.

So, we have:

[tex]5G + 4S + 2B = 26[/tex] -- (1)

[tex]4G + 4S + 4B = 26[/tex] -- (2)

[tex]3G + 4S + 6B = 26[/tex] -- (3)

Divide both sides of (2) by 2

[tex]4G + 4S + 4B = 26[/tex]

[tex]2G + 2S + 2B = 13[/tex]

So, the system of equations are:

[tex]5G + 4S + 2B = 26[/tex]

[tex]2G + 2S + 2B = 13[/tex]

[tex]3G + 4S + 6B = 26[/tex]

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