Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be 9 round tables and 11 rectangular tables, which will require a total of 51 centerpieces. On the left side, there will be 9 round tables and 10 rectangular tables, for which they will need to assemble a total of 48 centerpieces. How many centerpieces will be on each table? There will be _____ centerpieces on every round table and _____ centerpieces on every rectangular one.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be 9 round tables and  11 rectangular tables, which will require a total of 51 centerpieces. On the left side, there will be 9 round tables and  10 rectangular tables, for which they will need to assemble a total of 48 centerpieces. How many centerpieces will be on each table?  There will be _____ centerpieces on every round table and _____ centerpieces on every rectangular one.

Bytelearn · Accepted Answer

Set up equations: Let's denote the number of centerpieces on every round table as 'r' and on every rectangular table as 't'. We need to set up two equations based on the information given. On the right side of the room, there are 9 round tables and 11 rectangular tables requiring a total of 51 centerpieces. This gives us the equation: 9r + 11t = 51Solve first equation: On the left side of the room, there are 9 round tables and 10 rectangular tables needing a total of 48 centerpieces. This gives us the second equation: 9r + 10t = 48Eliminate variable: We now have a system of two equations with two variables: 9r + 11t = 51 9r + 10t = 48 To solve this system, we can subtract the second equation from the first to eliminate 'r' and solve for 't'. (9r + 11t) - (9r + 10t) = 51 - 48 9r + 11t - 9r - 10t = 3 t = 3Substitute back to solve: Now that we have the value for 't', we can substitute it back into one of the original equations to solve for 'r'. We'll use the second equation for this purpose: 9r + 10(3) = 48 9r + 30 = 48 9r = 48 - 30 9r = 18 r = 18 / 9 r = 2

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