Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 3 • Question 11

Trey opens a bank account with a starting balance of £400. Based on his spending habits, here is a formula to estimate the amount of money in Trey’s bank account: 𝑚 = −8𝑑 + 400. 𝑚 is the amount of money in Trey’s bank account, given in pounds. 𝑑 is the number of days after Trey opens the bank account. a) Estimate the amount of money in Trey’s bank account 40 days after he opens it. b) The bank will close Trey’s account if his balance reaches zero. Trey’s friend says, “Given Trey’s current spending habits, the bank will close his account 60 days after he opens it.” Is Trey’s friend correct? Give reasons for your answer.

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Video Transcript

Trey opens a bank account with a starting balance of 400 pounds. Based on his spending habits, here is a formula to estimate the amount of money in Trey’s bank account. 𝑚 is equal to negative eight 𝑑 plus 400. 𝑚 is the amount of money in Trey’s bank account, given in pounds. 𝑑 is the number of days after Trey opens the bank account. Part a), estimate the amount of money in Trey’s bank account 40 days after he opens it.

There is also a part b) that we will look at later. We’re given the formula that 𝑚 is equal to negative eight 𝑑 plus 400. As 𝑑 stands for the number of days, to calculate the money at any time, we need to multiply the number of days by negative eight and then add 400. We want to estimate the amount of money in Trey’s bank account after 40 days. This means that 𝑑 is equal to 40. Therefore, 𝑚 is equal to negative eight multiplied by 40 plus 400. Multiplying a negative number by a positive number gives a negative answer. As eight multiplied by 40 is 320, negative eight multiplied by 40 is equal to negative 320. We need to add 400 to negative 320. This is equal to 80. Therefore, Trey has 80 pound in his bank account after 40 days. The second part of the question says the following.

b) The bank will close Trey’s account if his balance reaches zero. Trey’s friend says, “Given Trey’s current spending habits, the bank will close his account 60 days after he opens it.” Is Trey’s friend correct? Give reasons for your answer.

We’re told that the bank will close the account when the balance reaches zero. This means there will be no money in the account. Therefore, 𝑚 is equal to zero. Substituting this into our formula gives us zero is equal to negative eight 𝑑 plus 400. Adding eight 𝑑 to both sides of this equation gives us eight 𝑑 is equal to 400. Dividing both sides of this equation will enable us to calculate the number of days it will take till his balance reaches zero. Eight 𝑑 divided by eight is equal to 𝑑. And 400 divided by eight is equal to 50, as 40 divided by eight equals five. We can, therefore, conclude that Trey’s friend is not correct, as the balance will be zero after 50 days and not 60. If Trey continues his current spending habits, his friend thought his account will close after 60 days. Whereas in reality, it will close after 50 days.

An alternative method would be to have substituted 𝑑 equals 60 into the formula. This would give us 𝑚 is equal to negative eight multiplied by 60 plus 400. Negative eight multiplied by 60 is equal to negative 480. Adding 400 to this gives us an answer of negative 80. As this is not equal to zero, once again, we can see that his friend was not correct.

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