Question

Liam is setting up folding chairs for a meeting. If he arranges the chairs in 7 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 5 rows of that same length, he has 17 left over. How many chairs does Liam have?

Answer 1

Answer: 47

Step-by-step explanation: Let's call the number of chairs Liam has x. We can set up the following equations to represent the problem:

7r = x - 5

5r = x - 17

Where r is the length of each row.

To solve for x, we can set the two equations equal to each other:

7r = x - 5

5r = x - 17

Then we can solve for x by combining like terms and solving for the value of x:

7r - 5r = x - 5 - x + 17

2r = 12

r = 6

We can substitute the value of r back into either of the original equations to solve for x:

7r = x - 5

7 * 6 = x - 5

x = 47

Therefore, Liam has 47 chairs.