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Amrit’s income is 32% more than Bethan’s income - OCR - GCSE Maths - Question 20 - 2019 - Paper 1

Question 20

Amrit’s income is 32% more than Bethan’s income. Amrit and Bethan’s combined income is £54,868. Calculate Amrit’s income.

Worked Solution & Example Answer:Amrit’s income is 32% more than Bethan’s income - OCR - GCSE Maths - Question 20 - 2019 - Paper 1

Step 1

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Answer

Let Bethan's income be denoted as $B$ . Then, Amrit's income, denoted as $A$ , can be expressed as:

$A = B + 0.32B = 1.32B$

Step 2

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Answer

The combined income of Amrit and Bethan is given as £54,868. Therefore, we can set up the equation:

$A + B = 54868$

Substituting for $A$ , we have:

$1.32B + B = 54868$

Step 3

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Answer

Combining like terms gives:

$2.32B = 54868$

To isolate $B$ , divide both sides by 2.32:

$B = \frac{54868}{2.32} = 23659.48$

Step 4

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Answer

Now, substituting back to find Amrit's income:

$A = 1.32B = 1.32 \times 23659.48 = 31208.52$

Thus, Amrit's income is approximately £31,208.52.

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