Question

Hue is arranging chairs.She can form 6 rows of a given length with 3 chairs left over,or 8 rows of that same length if she gets 11 more chairs.Write and solve an equation to find how many chairs are in that row length

Answer 1

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.

$y=6x+3 \ \ \ \ \ equation \ 1$

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.

$y=8x-11 \ \ \ \ \ equation \ 2$

From equation 1 and equation 2 we can say that L.H.S is same.

So according to law of transitivity we get;

$6x+3=8x-11$

Combining like terms we get;

$8x-6x=11+3$

Using Subtraction and Addition property we get;

$2x=14$

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

$\frac{2x}{2}=\frac{14}{2}\\\\x=7$

Hence there are 7 chairs in each row length.