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 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 the initial number of stamps

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Answer

Let the number of Tom's stamps be represented as 3x and Adam's stamps as 7x. Given that the total is 240 stamps, we can set up the equation:

$3x + 7x = 240$

This simplifies to:

$10x = 240$

Thus, we find that:

$x = 24$

Therefore, Tom initially has:

$3x = 3(24) = 72$

And Adam initially has:

$7x = 7(24) = 168$ .

Step 2

Set up the equation after Tom buys stamps

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Answer

Let the number of stamps Tom buys from Adam be represented as y. After the transaction, Tom's number of stamps is:

$72 + y$

And Adam's number of stamps becomes:

$168 - y$ .

According to the new ratio, we have:

$\frac{72 + y}{168 - y} = \frac{3}{5}$ .

Step 3

Cross-multiply to solve for y

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Cross-multiplying gives:

$5(72 + y) = 3(168 - y)$

Expanding both sides results in:

$360 + 5y = 504 - 3y$ .

Combining like terms leads to:

$8y = 144$ .

Finally, dividing by 8 yields:

$y = 18$ .

Step 4

Conclusion

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Answer

Tom buys 18 stamps from Adam.

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