Tuesday Tangle Solution

Gentle Reader,

As promised, here is the solution to yesterday's Tangle brainteaser. If you haven't already seen the Tuesday Tangle, check out the post below before reading on.

Solution to Sing a Song of Sixpence... er, Six Dollars: 

To find the amount of seats in the Erewhon Town Hall for Selene's concert, we must first work out the difference in takings from Saturday to Sunday. This extra money must represent the ticket price increase, which we know equals $4 extra, for every seat in the fourth row. The ticket prices in all the other rows remained the same.

We know that the difference in takings from Saturday to Sunday is $80. This extra profit represents the additional money gained for Row Four. The first night, Row Four was only $6 per seat, and the second night it was $10 per seat. Taking this into account, we know that Row Four brought it an extra $4 per seat.

So, we take the extra profit ($80) and divide it by the profit per seat in Row Four ($4). This gives us 20, which is therefore the number of seats in Row Four.

We know that all rows had the same number of seats, so therefore each row had 20 seats.

Now we must work out how many seats there were in total.

We know that, on Sunday, there were four rows with 20 seats (totalling 80), which charged $10 each. Therefore Selene got $800 from these seats.

Deducting $800 from the overall takings of Sunday night (which was $2120), we get $1320. This represents the takings from all the other seats (Row five and backwards). 

If we divide the takings from Row Five and backwards, $1320, by the ticket price, $6, we get 220. This is the number of seats there are from Row Five and backwards.

Therefore, we have 80 seats in the first four rows, and 220 seats in the rest of the hall. This means that there were 300 seats (and 15 rows) in total in the Erewhon Town Hall for Selene’s concerts.

So, Gentle Reader, how did you go?