Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 3 • Question 13

The height of a wall is increased by 1/6. The new height of the wall is 4.2 m. Calculate the original height of the wall.

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Video Transcript

The height of a wall is increased by one-sixth. The new height of the wall is 4.2 metres. Calculate the original height of the wall.

We have a wall whose height is increased by one-sixth. And then, the new height of the wall is 4.2 metres. And we want to calculate 𝑥, the original height of the wall.

If 𝑥 is the original height, then 𝑥 multiplied by some multiplier will equal our new height. We can plug in 4.2 for the new height. Bring down our 𝑥.

Looking back at our diagram, the original height of the wall can be written as a fraction of one, six over six. And that means our multiplier will be the six-sixths from the original height plus the one-sixth increase. Our multiplier is seven-sixths.

So seven sixths 𝑥 equals 4.2. To solve for 𝑥, we’ll need to get it by itself. We can do that by multiplying seven-sixths 𝑥 by six over seven. And if we do that on the left of our equation, we have to do it on the right side as well.

On the left, everything cancels out, leaving us with 𝑥. On the right side, 4.2 times six and then divided by seven equals 3.6.

The original height of the wall was 3.6 meters.

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