Question

Hue is arranging chairs. She can form 2 rows of a given length with 2 chairs left over, or 6 rows of that same length if she gets 14 more chairs. Complete the equation and solve it to find how many chairs are in that row length. In your equation, use the variable x to represent the number of chairs in each row.

Answer 1

There are 7 chairs in each row length.
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.

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.

From equation 1 and equation 2 we can say that L.H.S is same.
So according to law of transitivity we get;

Combining like terms we get;

Using Subtraction and Addition property we get;

Now Using Division Property we will divide both side by 2.

Hence there are 7 chairs in each row length.