
I have some tables and chairs. If I place two chairs at each table, I have one extra chair. If I place three chairs at each table, I have one table with no chairs. What is the sum of the total number of tables and chairs?
A) 12
B) 7
C) 17
D) 13
Answer
475.5k+ views
Hint:
Here, we will assume the number of tables and chairs to be any variable. We will frame two linear equations with two variables using the given information. Then we will equate these linear equations and find the number of chairs and tables. We will then find the total sum by adding the number of tables and number of chairs.
Complete step by step solution:
Let be the number of chairs and be the number of tables.
If two chairs are placed at each table, then one extra chair is left without placed at the table. So, we get
……………………………………………
If three chairs are placed at each table, then one table is left without a chair. So, we get
…………………………………………
Now, by equating the equation and equation , we get
By multiplying the terms, we get
By rewriting the equation, we get
By adding and subtracting the like terms, we get
So, the Number of Tables is .
By substituting the number of tables in the equation , we get
Multiplying the terms, we get
Adding the terms, we get
So, the Number of Chairs is
Now, we will find the total number of chairs and tables by adding the number of chairs and the number of tables.
Total Number of Chairs and Tables Number of Chairs Number of Tables
Substituting the values in the above equation, we get
Total Number of Chairs and Tables
Adding the terms, we get
Total Number of Chairs and Tables
Therefore, the total number of chairs and tables is 13.
Thus, option (4) is the correct answer.
Note:
Linear equations are a combination of constants and variables. A linear equation is defined as an equation with the highest degree as 1 and it has only one solution. Here, we can make a mistake by just finding the numbers of chairs and tables and forget to find the total number of chairs and tables. We can make mistakes in framing the equation and thus end up getting the wrong answer.
Here, we will assume the number of tables and chairs to be any variable. We will frame two linear equations with two variables using the given information. Then we will equate these linear equations and find the number of chairs and tables. We will then find the total sum by adding the number of tables and number of chairs.
Complete step by step solution:
Let
If two chairs are placed at each table, then one extra chair is left without placed at the table. So, we get
If three chairs are placed at each table, then one table is left without a chair. So, we get
Now, by equating the equation
By multiplying the terms, we get
By rewriting the equation, we get
By adding and subtracting the like terms, we get
So, the Number of Tables is
By substituting the number of tables in the equation
Multiplying the terms, we get
Adding the terms, we get
So, the Number of Chairs is
Now, we will find the total number of chairs and tables by adding the number of chairs and the number of tables.
Total Number of Chairs and Tables
Substituting the values in the above equation, we get
Adding the terms, we get
Therefore, the total number of chairs and tables is 13.
Thus, option (4) is the correct answer.
Note:
Linear equations are a combination of constants and variables. A linear equation is defined as an equation with the highest degree as 1 and it has only one solution. Here, we can make a mistake by just finding the numbers of chairs and tables and forget to find the total number of chairs and tables. We can make mistakes in framing the equation and thus end up getting the wrong answer.
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