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 silver, and 6 bronze replicas. Which system of equations may be used to find the price, in dollars of each type of replica? A ) 5x+4y+3z=26 4x+4y+4z=26 2x+4y+6z=26 B ) 5x+4y+2z=26 4x+4y+4z=26 3x+4y+6z=26 C ) 5x+4x+2x=26 4y+4y+4y=26 3z+4z+6z=26 D ) 5+4+3=26x 4+4+4=26y 2+4+6=26z

To find the price of each type of replica, we need to set up a system of equations based on the given information.<br /><br />Let's denote the price of a gold replica as x, the price of a silver replica as y, and the price of z.<br /><br />From the given information, we can set up the following equations:<br /><br />1. For the package containing 5 gold, 4 silver, and 2 bronze replicas, the total cost is $26:<br /> 5x + 4y + 2z = 26<br /><br />2. For the package containing 4 gold, 4 silver, and 4 bronze replicas, the total cost is $26:<br /> 4x + 4y + 4z = 26<br /><br />3. For the package containing 3 gold, 6 silver, and 6 bronze replicas, the total cost is $26:<br /> 3x + 6y + 6z = 26<br /><br />Therefore, the correct system of equations is:<br /><br />B<br />$\{ \begin{5x+4y+2z=26\\ 4x+4y+4z=26\\ 3x+6y+6z=26\end{matrix} $