Tom and Adam have a total of 240 stamps. The ratio of the number of Tom’s stamps to the number of Adam’s stamps is 3:7 Tom buys some stamps from Adam. The ratio of the number of Tom’s stamps to the number of Adam’s stamps is now 3:5 How many stamps does Tom buy from Adam? You must show all your working.

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Tom and Adam have a total of 240 stamps - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Question 4

Tom and Adam have a total of 240 stamps. The ratio of the number of Tom’s stamps to the number of Adam’s stamps is 3:7 Tom buys some stamps from Adam. The ratio of ... show full transcript

Worked Solution & Example Answer:Tom and Adam have a total of 240 stamps - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Step 1

Determine Initial Amounts of Stamps

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Answer

Let the number of Tom's stamps be represented as $3x$ and the number of Adam's stamps as $7x$ based on the initial ratio 3:7. Then, we know that the total number of stamps is: $3x + 7x = 240$ This simplifies to: $10x = 240$ Solving for $x$ , we get: $x = 24$ Thus, Tom has: $3x = 3(24) = 72$ stamps and Adam has: $7x = 7(24) = 168$ stamps.

Step 2

Calculate the New Ratio after Tom Buys Stamps

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After Tom buys some stamps from Adam, let the number of stamps Tom buys be $y$ . The new amounts of stamps are:

Tom's: $72 + y$
Adam's: $168 - y$

Given that the new ratio of Tom's stamps to Adam's stamps is 3:5, we can set up the equation: $\frac{72 + y}{168 - y} = \frac{3}{5}$ Cross-multiplying gives: $5(72 + y) = 3(168 - y)$ Expanding and simplifying leads to: $360 + 5y = 504 - 3y$ Combining like terms yields: $8y = 144$ Thus: $y = 18$ .

Step 3

Final Answer

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Answer

Tom buys 18 stamps from Adam.

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