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Last year, Katie earned £16,200 - OCR - GCSE Maths - Question 3 - 2017 - Paper 1

Question 3

Last year, Katie earned £16,200. Her total loan repayments were £6400. Katie estimates that the ratio of her loan repayments to her earnings is approximately 3 : 8.... show full transcript

Worked Solution & Example Answer:Last year, Katie earned £16,200 - OCR - GCSE Maths - Question 3 - 2017 - Paper 1

Step 1

Calculate the actual ratio of loan repayments to earnings

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Answer

To find the ratio of Katie's loan repayments to her earnings, we use the formula:

ext{Ratio} = rac{ ext{Loan Repayments}}{ ext{Earnings}} = rac{6400}{16200}

Now, we simplify this fraction:

Divide both the numerator and the denominator by 200:
- Loan Repayments: ( 6400 ÷ 200 = 32 )
- Earnings: ( 16200 ÷ 200 = 81 )

Thus, the ratio simplifies to( \frac{32}{81} ).

Step 2

Evaluate Katie's estimate of the ratio

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Answer

Katie's estimated ratio of loan repayments to earnings is 3 : 8, which can also be expressed as:

rac{3}{8} ext{ or } 3 \div 8 = 0.375

Now, we calculate the actual ratio we simplified, ( \frac{32}{81} ):

To find the decimal form, we divide 32 by 81:

32 ÷ 81 ≈ 0.395

When comparing 0.375 and 0.395, we see that they are not equal, indicating her estimate is not accurate.

Step 3

Conclusion

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Answer

Since the actual ratio ( \frac{32}{81} ) does not simplify down to approximately 3 : 8, Katie is incorrect in her estimation. Therefore, her assertion about the ratio of loan repayments to her earnings being approximately 3 : 8 is not correct.

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