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Mo's tyre pressure gauge shows a reading which is 12% higher than the actual pressure - OCR - GCSE Maths - Question 19 - 2017 - Paper 1

Question 19

Mo's tyre pressure gauge shows a reading which is 12% higher than the actual pressure. What is the actual pressure when Mo's gauge shows 38.64?

Worked Solution & Example Answer:Mo's tyre pressure gauge shows a reading which is 12% higher than the actual pressure - OCR - GCSE Maths - Question 19 - 2017 - Paper 1

Step 1

Calculate the percentage of the actual pressure

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Answer

Let the actual pressure be denoted as $P_{actual}$ . Since Mo's gauge reading is 12% higher than the actual pressure, we can express this relationship as:

$P_{gauge} = P_{actual} + 0.12P_{actual}$

This can be simplified to:

$P_{gauge} = 1.12P_{actual}$

Step 2

Substitute the gauge reading to find the actual pressure

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Answer

Substituting the given gauge reading of 38.64 into the equation:

$38.64 = 1.12P_{actual}$

To find $P_{actual}$ , we rearrange the equation:

$P_{actual} = \frac{38.64}{1.12}$

Step 3

Calculate the actual pressure

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Answer

Now performing the division:

$P_{actual} = 34.5$

Therefore, the actual pressure when Mo's gauge shows 38.64 is 34.5.

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