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Sundip and Emma have some money - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Question 7

Sundip and Emma have some money. The ratio of Sundip's money to Emma's money is 3 : 5. Emma spends £450 of her money. The ratio of Sundip's money to Emma's money is ... show full transcript

Worked Solution & Example Answer:Sundip and Emma have some money - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Step 1

Determine Initial Values

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Answer

Let Sundip's money be represented as $3x$ and Emma's money as $5x$ for some positive integer $x$ . This means:

Sundip: $3x$
Emma: $5x$

Step 2

Account for Emma's Spending

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Answer

After Emma spends £450, her new amount of money is:

$5x - 450$

Step 3

Set Up the New Ratio

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Answer

The new ratio of Sundip's money to Emma's money becomes:

$\frac{3x}{5x - 450} = \frac{2}{3}$

Cross-multiplying gives:

$3 \times 3x = 2 \times (5x - 450)$

Simplifying this yields:

$9x = 10x - 900$

Rearranging results in:

$900 = x$

Step 4

Calculate Sundip's Money

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Answer

Substituting $x = 900$ into Sundip's money equation:

$3x = 3 \times 900 = £2700$

Thus, Sundip has £2700.

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