### Video Transcript

Vicky has a credit card. This formula calculates the interest Vicky must pay to the bank each month based on her balance: 𝐼 is equal to negative 0.15 multiplied by 𝐵 plus 75. 𝐼 is the interest Vicky must pay and 𝐵 is Vicky’s credit card balance. Vicky only pays interest if 𝐼 is a positive number. Part a) How much interest must Vicky pay if she has a balance of negative 300 pound? There is also a part b and c that we will look at later.

We’re told in this part of the question that Vicky’s balance is negative 300 pounds. This means we must substitute this into the formula. Substituting 𝐵 equals negative 300 gives us 𝐼 is equal to negative 0.15 multiplied by negative 300 plus 75. Our first step using our order of operations is to calculate the sum inside the bracket. Negative 300 plus 75 is equal to negative 225. So we are left with 𝐼 is equal to negative 0.15 multiplied by negative 225. Typing this into our calculator gives us 33.75. Remember that when you multiply two negative numbers, you get a positive answer. The interest that Vicky has to pay if she has a balance of negative 300 pounds is 33 pounds and 75 pence.

The second part of the question says the following. b) What is the lowest balance that Vicky can have without paying interest?

We’re told that Vicky only pays interest if 𝐼 is a positive number. This means that 𝐼 needs to be greater than zero. As the interest needs to be greater than zero, we can also say that the other side of the formula must be greater than zero. Negative 0.15 multiplied by 𝐵 plus 75 is greater than zero. We can firstly divide both sides of this equation by negative 0.15. On the left-hand side, we’re left with 𝐵 plus 75 as anything divided by itself is equal to one. On the right-hand side, we still have zero. Dividing zero by any number also gives us zero. Our final step to solve the inequality is to subtract 75 from both sides of the equation. This gives us 𝐵 on the left-hand side and negative 75 on the right-hand side. If Vicky’s bank balance at the end of every month is greater than negative 75, she will not pay any interest. This means that the lowest balance that Vicky can have without paying interest is negative 75 pounds.

The final part of the question says the following. c) Vicky must pay 155 pound 73 pence interest this month. What is Vicky’s credit card balance?

In this part of the question, we’re given the interest 𝐼 and we’re asked to calculate the balance 𝐵. Substituting our value for 𝐼 into the formula gives us 155.73 is equal to negative 0.15 multiplied by 𝐵 plus 75. Once again, we can start here by dividing both sides of the equation by negative 0.15. This gives us negative 1038.2 on the left-hand side, as dividing a positive number by a negative number gives a negative answer. On the right-hand side, we’re left with 𝐵 plus 75. Our next step is to subtract 75 from both sides of the equation. Subtracting 75 from negative 1038.2 gives us negative 1113.2. As this is our value for 𝐵, we can say that Vicky’s credit card balance is negative 1113 pounds and 20 pence.