Invitations were sent one week before the big event. Replies started coming in the following Monday. On Tuesday 2 more replies had been received than on Monday. On Wednesday, 11 more than one half the number of replies received on Monday were received, If a total of 53 invitations were received during the first 3 days of that week, how many replies were received on Monday?

Ok so we know this.

Monday = x
Tuesday = x +2
Wednesday = (1/2)x +11
They all add up to 53. The equation should look like this:

(x) + (x + 2) + (1/2x + 11) = 53

To solve this problem, let's break it down step by step.

1. Let's call the number of replies received on Monday "x".
2. According to the problem, on Tuesday, 2 more replies were received than on Monday. So, the number of replies on Tuesday is "x + 2".
3. On Wednesday, 11 more than one-half the number of replies received on Monday were received. That means, Wednesday's replies can be expressed as "(1/2)x + 11".
4. The total number of replies received during the first three days (Monday, Tuesday, and Wednesday) is given as 53. So we can write the equation: x + (x + 2) + ((1/2)x + 11) = 53.
5. Simplifying this equation, we get: x + x + 2 + (1/2)x + 11 = 53.
6. Combining like terms, we have: (2.5)x + 13 = 53.
7. Subtracting 13 from both sides, we get: (2.5)x = 40.
8. Finally, divide both sides by 2.5 to find the value of x: x = 40/2.5 = 16.

Therefore, 16 replies were received on Monday.