Question

Hue is arranging chairs. She can form 3 rows of a given length with 5 chairs left over, or 6 rows of that same length if she gets 13 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

Answer: There are 6 chairs in each row.

Step-by-step explanation:

Since we have given that

Number of chairs in each row be x

3 rows of a given length with 5 chairs left over,

So, mathematically it is expressed as

$3x+5$

6 rows of that same length if she gets 13 more chairs.

Mathematically it is expressed as

$6x-13$

According to question, the number of chairs are same in both the cases,

So, we get that

$3x+5=6x-13\\\\5+13=6x-3x\\\\18=3x\\\\x=\dfrac{18}{3}\\\\x=6$

Hence, there are 6 chairs in each row.

Answer 2

By solving a system of equations we will see that there are 23 chairs.

How to find the number of chairs?

First, we define x as the number of chairs, using the given information we can see that:

When x is divided by 3 we have 5 chairs left.

When x is divided by 6 we need 13 chairs more to get the same length than before.

From the first restriction we can have:

x = n*3 + 5

From the second one:

x = n*6 - 13

Where n is the number of chairs in each row.

So we found a system of equations.

Then we need to solve:

x = n*3 + 5 = n*6 - 13

5 + 13 = n*6 - n*3

18 = n*3

18/3 = n

6 = n

Then the number of chairs is:

x = 3*n + 5 = 3*6 + 5 = 23

There are 23 chairs.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904