Write a system of equations to describe the situation below, solve using elimination, 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 1 round table and 3 rectangular tables, which will require a total of 10 centerpieces. On the left side, there will be 15 round tables and 2 rectangular tables, for which they will need to assemble a total of 21 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 elimination, 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 1 round table and  3 rectangular tables, which will require a total of 10 centerpieces. On the left side, there will be 15 round tables and  2 rectangular tables, for which they will need to assemble a total of 21 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

Define Variables: Let's denote the number of centerpieces on each round table as r and the number of centerpieces on each rectangular table as t. On the right side of the room, there is 1 round table and 3 rectangular tables, requiring a total of 10 centerpieces. This gives us the equation 1r + 3t = 10.Form Equations: On the left side of the room, there are 15 round tables and 2 rectangular tables, needing a total of 21 centerpieces. This gives us the equation 15r + 2t = 21.Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, r or t. We choose to eliminate t because its coefficients are smaller and easier to work with.Correct Subtraction: To eliminate t, we multiply the first equation by 2, the coefficient of t in the second equation. This gives us the new equation 2r + 6t = 20.We now subtract the new first equation from the second equation to eliminate t. This gives us 15r - 2r + 2t - 6t = 21 - 20, which simplifies to 13r - 4t = 1.We made a mistake in the previous step by not correctly subtracting the equations. Let's correct this. Subtracting the new first equation from the second equation should give us 15r + 2t - (2r + 6t) = 21 - 20, which simplifies to 13r - 4t = 1. However, we should have subtracted the entire first equation from the second equation, not just the r terms. Let's correct this and subtract the equations properly.

Full solution

More problems from Solve a system of equations using elimination: word problems

Related topics