# Video: KS2-M16 • Paper 2 • Question 12

If 𝑛 = 22, calculate 2𝑛 + 9. If 2𝑞 + 4 = 100, what is the value of 𝑞?

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### Video Transcript

If 𝑛 equals 22, calculate two 𝑛 plus nine. If two 𝑞 plus four equals 100, what is the value of 𝑞?

Let’s start by answering this part of the question. We know the value of 𝑛 is 22. We’re asked to calculate two 𝑛 plus nine. Two 𝑛 means multiply two by 𝑛. We know that 𝑛 is 22. So two 𝑛 is two multiplied by 22, which is 44. We’ve calculated two 𝑛. Now we just need to add nine. 44 plus nine is 53.

Now we can move on to the next part of the question where we’re asked to find the value of 𝑞. We’re told that two 𝑞 plus four is equal to 100. We can use this fact to help us sketch a bar model. Two times 𝑞 plus four is equal to 100. We can use this bar model to help us work back using the inverse to find the value of 𝑞.

If we take away the four, this will leave us with two 𝑞 or two lots of 𝑞. 100 take away four is 96. If two times 𝑞 or two lots of 𝑞 is 96, then one 𝑞 or the value of 𝑞 will be 96 divided by two. Half of 90 is 45 and half of six is three. 45 and three is 48. Half of 96 is 48. The value of 𝑞 is 48.