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Helen had to arrange some chairs in a fixed number of rows. If she put 8 chairs in each row, she would be short of 7 chairs. If she put 7 chairs in each row, she would have 2 chairs left. How many chairs were there?

Question

Helen had to arrange some chairs in a fixed number of rows. If she put 8 chairs in each row, she would be short of 7 chairs. If she put 7 chairs in each row, she would have 2 chairs left. How many chairs were there?

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Solution

Let's solve this problem step by step:

Step 1: Let's denote the number of rows as 'x' and the number of chairs as 'y'.

Step 2: From the problem, we have two equations. The first one is y = 8x - 7 (this is because if she put 8 chairs in each row, she would be short of 7 chairs). The second one is y = 7x + 2 (this is because if she put 7 chairs in each row, she would have 2 chairs left).

Step 3: Now we have a system of two equations, and we can solve it. Since both equations are equal to y, we can set them equal to each other: 8x - 7 = 7x + 2.

Step 4: Solve this equation for x. Subtract 7x from both sides to get x = 9.

Step 5: Substitute x = 9 into the first equation to find y: y = 8*9 - 7 = 65.

So, there were 65 chairs.

This problem has been solved

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