Answer:
There are 7 chairs in each row length.
Step-by-step explanation:
Let number of chairs in 1 row be 'x'.
Let total number of chairs be 'y'.
Given:
Hue can form 6 rows of a given length with 3 chairs left over.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 6 plus number of chairs which is left which is 3.
Framing in equation form we get.
![y=6x+3 \ \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=y%3D6x%2B3%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Also Given:
Hue can form 8 rows of that same length if she gets 11 more chairs.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 8 minus number of chairs which is required more which is 11.
Framing in equation form we get.
![y=8x-11 \ \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=y%3D8x-11%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
From equation 1 and equation 2 we can say that L.H.S is same.
So according to law of transitivity we get;
![6x+3=8x-11](https://tex.z-dn.net/?f=6x%2B3%3D8x-11)
Combining like terms we get;
![8x-6x=11+3](https://tex.z-dn.net/?f=8x-6x%3D11%2B3)
Using Subtraction and Addition property we get;
![2x=14](https://tex.z-dn.net/?f=2x%3D14)
Now Using Division Property we will divide both side by 2.
![\frac{2x}{2}=\frac{14}{2}\\\\x=7](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B14%7D%7B2%7D%5C%5C%5C%5Cx%3D7)
Hence there are 7 chairs in each row length.