Last year, Jacob went to four concerts. Three of his tickets cost five pound each. The other ticket cost seven pound. What was the mean cost of the tickets?
In this problem, we’re not being asked for the total cost of the tickets. We’re being asked for the mean cost. But what does the word “mean” mean? The mean is a way of calculating the average of a set of information or data. In this problem, we’re talking about the cost of tickets. There’re two steps to calculating the mean. Step one is to find the total of all the different values. And step two is to divide this total by the number of values or the number of numbers that we’ve added together.
So if we think about this problem, finding the total means finding the total cost of all the tickets that Jacob bought. And then, dividing by the number of values means dividing by the number of tickets that Jacob bought. And so the mean cost is the total cost divided by the number of tickets.
Now that we know what we need to do to calculate the answer, let’s read the question again. We’re told that Jacob went to four concerts. But what was the total cost of all of his tickets? Three of his tickets cost five pound each. Notice that this says five pounds each and not five pounds altogether. So to calculate the total of those three tickets, we need to multiply three by five. We’re told that the fourth ticket cost seven pound. And so after multiplying, we also need to add seven. Three times five equals 15. So those first three tickets cost 15 pounds altogether. And then if we add seven, we get an answer of 22. The total cost of all the tickets was 22 pounds.
Remember, to find the mean costs, we need to divide this amount by the number of tickets. We know from the first fact that Jacob went to four concerts. And so we know he’s bought four tickets. And so to calculate the mean cost, we now know that we need to work out the answer to 22 pounds divided by four. How can we split 22 into four?
There are two quick ways we could do this. The first is if we understand that halving and then halving again is the same as dividing by four, think of a shape where we halve it and then halve it again to get four equal parts. It’s just the same with numbers. Half of 22 or 22 divided by two equals 11. And then half of 11 or 11 divided by two equals five and a half or 5.5. So we can say that 22 pounds divided by four equals 5.5 pounds or five pounds 50.
Another quick way to divide 22 pounds by four is to partition 22 pounds into 20 pounds and two pounds. 20 pounds divided by four equals five pounds. And two pounds divided by four equals 50 pence. Five pounds and 50 pence equals five pound 50. Although it looks like there were only two steps that we needed to do to find the answer, perhaps there were three.
The first step was nothing to do with calculating. It was all about understanding what the mean cost means. Once we understood how to calculate the mean, we were well on the way to finding the answer. And then there were only two steps left. We knew that, to find the mean, we need to divide the total cost by the number of tickets. So to start with, we found the total of all the different values. Three lots of five pounds plus one lot of seven pounds. And we worked this out as 22 pounds in total that Jacob spent on tickets. We knew that the number of tickets that Jacob bought was four. So we needed to divide 22 by four to find the answer.
On average, Jacob spent five pound 50 per ticket. In other words and in answer to the problem, the mean cost of the tickets was five pounds 50.