Olivia buys three packets of nuts. She pays with a two-pound coin. This is her change. What is the cost of one packet of nuts?
In this problem, we’re told that Olivia buys three packets of nuts. We’re asked to calculate the cost of one of those packets of nuts. The way that we can do this is to somehow find the total of all three packets of nuts and then divide that total by three to find the cost of one packet. But we’re not told how much three packets of nuts cost altogether. How can we work out this amount?
We’re given two pieces of information to help us. The first is the coin that Olivia pays with. She pays using a two-pound coin. This has a value of 200 pence. We’re also shown an image of the change that Olivia gets. And we can use this information to work out how much she spends on the packets of nuts. Let’s count how much her change is.
Start with 50 p; 50 add 20 equals 70 p. 70 plus 10 equals 80 p. Add another 10 p coin equals 90 p. And then add the final five pence to give us a total amount of change of 95 p. We know that Olivia pays with two pounds or 200 pence and that she has 95 pence change. So we can use these two facts now to work out how much she spends on the three packets of nuts.
200 take away 95 equals 105. So we can say that the total amount that Olivia spends on the three packets is 105 p which is the same as one pound five. Let’s divide this amount by three to find out the cost of one packet of nuts. Rather than divide a decimal by three, let’s work with the amounts of pence, 105.
How many threes are in 105? The first digit is too small. There are no threes in one. So let’s look at the first two digits instead. How many threes are in 10? Three, six, nine, three threes make nine. And we have a remainder of one. So we write that next to the five. How many threes are in 15? Three, six, nine, 12, 15, that was five threes. So if we split 105 into three equal parts, we get 35. Remember, that 35 stands for 35 p. So we can write the answer in one of two way. 35 p or 0.35 pounds which is exactly the same as 35 pence.
How did we find the answer? First, we wanted to calculate the total cost of the three packets of nuts. We weren’t told this total. But we were told the coin that Olivia used. And we were shown the change that she was given. So we added up the change and then subtracted this from the value of the coin to find the total amount that Olivia spent.
We could do this mentally. Then all we had to do was divide this overall total by three to find out the cost of one packet of nuts. We chose to divide 105 and not 1.05 because it’s a little bit easier to divide a whole number than a decimal. And so the cost of one packet of nuts equals 35 p. Or if we want to write it as pounds, 0.35 pounds.