Liam is setting up folding chairs for a meeting. If he arranges the chairs in 5 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 3 rows of that same length, he has 15 left over. How many
chairs does Liam have?
Liam has
chairs.

30 Chairs

Step-by-step explanation:

I will solve this problem using algebra and try to explain in detail.

We can form two equations with the information given to us.

Firstly, 5 times a length of chairs (I will call this unknown length of chairs x), plus 5 left over chairs, equals the total number of chairs (I will call the total number of chairs y).

5x + 5 = y

Secondly, 3 times a length of chairs (I will call this unknown length of chairs x), plus 15 left over chairs, equals the total number of chairs (I will call the total number of chairs y).

3x + 15 = y

Since both equations are equal to y, they are equal to each other

5x + 5 = 3x + 15

Take 5 away from both sides of the equals, and take away 3x from both sides of the equals

5x - 3x = 15 - 5

2x = 10

Divide both sides by 2

x = 5 chairs

Put this back into either the first equation or the second to solve for y

3 (5) + 15 = y

15 + 15 = y

y = 30 chairs