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Amrit's income is 32% more than Bethan's income - OCR - GCSE Maths - Question 2 - 2019 - Paper 1
Question 2
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 2 - 2019 - Paper 1
Step 1
Calculate Bethan's income based on combined income
Answer
Let Bethan's income be denoted as ( B ). According to the problem, Amrit's income ( A ) can be expressed as: [ A = B + 0.32B = 1.32B ]
The combined income of Amrit and Bethan is given as £54,868:
[ A + B = 54868 ]
Substituting the expression for ( A ) into the equation, we have:
[ 1.32B + B = 54868 ]
[ 2.32B = 54868 ]
Now we solve for ( B ):
[ B = \frac{54868}{2.32} ]
Step 2
Calculate Amrit's income using Bethan's income
Answer
Now that we have ( B ), we can find Amrit's income using the previously established relationship: [ A = 1.32B ] First, calculate ( B ): [ B = \frac{54868}{2.32} \ ext{So } B = 23,618 ] Now, substituting ( B ) to find ( A ): [ A = 1.32 \times 23618 ] [ A = 31,250.16 ] Thus, Amrit's income is approximately ( £31,250 ).