# Video: AF5P1-Q11-287147465976

Sunny has ten coins in her purse. She takes nine of the coins out of the purse. The most that she could take is £5.60. The least that she could take is £4.65. How much money does Sunny have in her purse?

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### Video Transcript

Sunny has 10 coins in her purse. She takes nine of the coins out of the purse. The most that she could take is five pounds 60 pence. The least that she could take is four pounds 65 pence. How much money does Sunny have in her purse?

There is quite a bit of information in this question. So it is important we read it carefully. We are told that Sunny has 10 coins altogether in the purse. Let’s assume that they are lined up from smallest value coin to largest value coin. We’re told that she takes nine of the coins out of the purse. The most that she can take out is five pounds 60. This would mean that she left the smallest value coin in the purse. We are also told that the least she can take out is four pounds and 65 pence. This would involve taking all the coins with the exception of the largest value coin.

In both of these cases, the eight middle value coins, everything apart from the smallest value and the largest value, are taken out of the purse. The difference between the two values can be calculated by subtracting four pounds and 65 pence from five pounds 60 pence. This is equal to 95 pence. We can, therefore, say the difference in value between the largest coin and the smallest coin is 95 pence. The only coins that we have in the UK are one pence, two pence, five pence, 10 pence, 20 pence, 50 pence, one pound, and two pounds. The two coins that have a difference of 95 pence are the one pound coin and a five pence coin.

We can, therefore, say that the largest coin in Sunny’s purse is a one-pound coin and the smallest coin was a five-pence coin. We now have two ways of calculating how much money Sunny has in her purse. The most amount that she had was five pounds 60. This was when the smallest coin was missing. We can, therefore, add five pence to five pounds 60. This gives us a total of pounds five pounds and 65 pence. Alternatively, the least amount that Sunny took out was four pounds 65. This was when the one-pound coin was missing. Adding four pounds 65 and one pound, once again, gives us five pound 65. The total amount of money that Sunny has in her purse is five pounds and 65 pence.