The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5 - Edexcel - GCSE Maths - Question 16 - 2022 - Paper 2
Question 16
The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5.
Both Marta and Khalid get an increase of £1.50 in their hourly pay.
The ratio of Marta’s hourly pay ... show full transcript
Worked Solution & Example Answer:The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5 - Edexcel - GCSE Maths - Question 16 - 2022 - Paper 2
Step 1
Set up the initial ratios
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Answer
Let Marta's initial pay be represented as 6x and Khalid's initial pay as 5x where x is a common factor. This sets up the ratio of their pays correctly.
Step 2
Calculate their new pays after the increase
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Answer
After both receive an increase of £1.50, Marta's pay becomes 6x+1.5 and Khalid's pay becomes 5x+1.5.
Step 3
Set up the equation based on the new ratio
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Answer
According to the problem, the new ratio is given as 13 : 11. This leads to the equation:
5x+1.56x+1.5=1113
Step 4
Solve for x
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Answer
Cross multiplying gives:
11(6x+1.5)=13(5x+1.5)
Expanding both sides results in:
66x+16.5=65x+19.5
Rearranging this gives:
66x−65x=19.5−16.5
Thus:
x=3
Step 5
Find the initial hourly pays
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Answer
Now plug the value of x back into the expressions for their initial pays:
