Hello,
I need help in solving the problem below. I understand that we have an inequality of 10 < x < 40, but I am stuck what to do afterwords.
I believe this solves it. We use the two statements to set up a system of equations with x and y. This allows us to prove the relationship between x and y numerically. This is just supporting an instinctive understanding that the number of people should be 3 + a multiple of both 4 and 5.
Once we determine 4x = 5y, lets plug in values of x and y and see what the resulting “A” or total # of people would be. Here, it only makes sense to be 23 due to the 10< A < 40 restrictions. Once we grasp that there are 23 people, then the # of people at the one table with < 6 people is just the remainder left over after diving 23/6. Thus it should be 5 people.
Hope this helps.
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I just wanna add that the intuition here is that when there is one table with 3 people, then the remaining # of people can be evenly split into tables of 5 each or tables of 4 each. So, the remaining people should be a common multiple of 4 and 5. Then we need to add the original 3 back in.