A plane has 46 rows and eight seats in each row. Adult tickets cost 250 pounds. Child tickets cost 150 pounds. All of the tickets for the flight were sold. Exactly 75 child tickets were sold. Orie estimates that the total amount of money made from ticket sales was 85000 pounds. Is Orie’s estimate close to the exact amount of money made from ticket sales for this flight? You must show your working.
If we want to know if Orie’s estimate is close to the exact amount of money made from ticket sales, then we need to be able to calculate the exact amount of money made from ticket sales. The amount of money made depends on how many and what type of tickets were sold. We’re given the information that all the tickets for the flight are sold. But we’re not told exactly how many seats are on this flight. We know that there are eight seats in each row and that the plane has 46 rows.
To calculate the total number of seats, we’ll need to multiply the number of rows by the number of seats in each row. We’ll need to multiply 46 by eight. We could line this up and do long multiplication. However, in this case, there’s an easier approach. We can break up the number 46 into two pieces that are easier to multiply by eight and then add each of these products together. Four times eight equals 32 and we add that zero. 40 times eight equals 320. Six times eight equals 48. Now, we add 320 and 48 together and we get 368.
Remember 368 tells us how many seats there are on this flight. To find out how much money was made, we’ll need to know how many of the seats were for children and how many of the seats were for adults. We’ve been told that 75 of the tickets were for children. If we take the number of seats on our flight 368 and subtract the number of child tickets that were sold, we’ll find the number of adult tickets that were sold. The best way to solve this problem is probably to line them up vertically and do subtraction this way.
Eight minus five is three. We need to borrow from our three. And then, we’ll subtract seven from 16 which is nine and bring down our two. This tells us that there were 293 adult tickets sold. Now that we know how many of each type of tickets were sold, we can calculate how much money was made from each type. There were 75 child tickets sold at a rate of 150 pounds each. Again, we can break up this multiplication to make it a little bit easier. We can multiply 70 by 150 and then five by 150 and then add those together. Seven times 15 equals 105. And then, we add the two zeros from 70 and from 150 which means 70 times 150 equals 10500. Next, we’ll multiply five times 15. Five times 15 equals 75. And we’ll bring over our zero. So we’ll have 10500 plus 750.
When we add these together, five plus seven equals 12. Bring up your one. One plus zero equals one. Bring down our one. The amount of money made from child ticket sales is then 11250 pounds. We can follow the same procedure for the adults. 293 adult tickets were sold at a rate of 250 pounds each. But how should we break this problem up?
We could try 200 times 250 plus 93 times 250. But multiplying 93 by 25 is not particularly easy. Another strategy would be to multiply 300 times 250 and then subtract seven times 250. We know that 293 is seven less than 300. And this set of multiplication will be much simpler. Three times 25 equals 75 and then bring over our three zeros. Seven times 25 equals 175 and we have one zero. To calculate this, we now need to subtract 1750 from 75000. Zero minus zero, we can’t subtract five from zero. And we can’t borrow from the next digit to the left because it’s zero. But we could borrow from 50. We’ll make that 49 and bring a one over. 10 minus five is five, nine minus seven is two, four minus one is three, and we’ll bring down our seven. The total amount of money made from adult ticket sales is 73250 pounds.
And to find the exact amount of money made from ticket sales, we need to add 73250 to 11250. When we do that, we get 84500. And we’ll do a comparison. Total ticket sales 84500, Orie’s estimate 85000. The difference here is 500 pounds. So we say that Orie’s estimate is within 500 pounds of the exact answer. And that it is a good estimate.