Mixed average questions

A stall sold 8, 0, 9 and 3 pies on the first 4 days. After the fifth day, the average number of pies sold in a day was 6. How many pies were sold on the fifth day? Try it first. Pause if you like. We want the fifth day. Those pies are inside the total for all 5 days, and so are the first 4 days'. So if we had both totals, taking one off the other leaves the fifth day. The first 4 days we can add up. 8 plus 0 plus 9 plus 3 is 20 pies. That 20 is 4 days' worth. But the average we're given isn't for those 4 days. It's for all 5. Different days, different total. And 6 pies a day is the only thing that can give us this one. And the day with none is still a day, so that is 4 days, and the fifth makes 5. 6 times 5 is 30 pies. Now we have both totals. 30 minus 20 is 10. So 10 pies were sold on the fifth day. An average is a total shared out over how many there are. Share the 30 across the 5 days, and every day comes to 6. There are two totals here, because there are two counts, 4 days and then 5. One we added up, and the other one the average gave us. And a day with none is one of them.