Maths: Question on Ratios, proportions, and percentages

[Kaushik]

Homework Statement

Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworks to Geoffrey, then Amal and Geoffrey will have in a 2:3 ratio. If Julia has 1/5th as many as Geoffrey (after Amal gives half his fireworks to Geoffrey), then what is the ratio of the number of fireworks Amal has to the number of fireworks Julia has?

Relevant Equations

Check the figure

Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworks to Geoffrey, then Amal and Geoffrey will have in a 2:3 ratio. If Julia has 1/5th as many as Geoffrey (after Amal gives half his fireworks to Geoffrey), then what is the ratio of the number of fireworks Amal has to the number of fireworks Julia has?

My attempt is given below

[Moderator's note: Moved from a technical forum and thus no template.]

 

[mfb]

Looks good for the final ratio, but the problem statement might ask about the original ratio (otherwise the information about giving fireworks away wouldn't matter and you could directly use the final ratios).

 

[Kaushik]

otherwise the information about giving fireworks away wouldn't matter and you could directly use the final ratios

I am not sure I understand this part.

When I read the question, I interpret the problem statement as asking for the final ratio. Where exactly am I misinterpreting it?

 

[PeroK]

I am not sure I understand this part.

When I read the question, I interpret the problem statement as asking for the final ratio. Where exactly am I misinterpreting it?

I agree with your solution. If you change the question to the initial ration, then it's 20:3.

You can put in some numbers to see the book solution is wrong.

 

[Kaushik]

I agree with your solution. If you change the question to the initial ration, then it's 20:3.

You can put in some numbers to see the book solution is wrong.

Are they asking us to find initial ration or final ration? According to the book solution, they found the final ration. But when I read it, I feel like they are asking for the initial ration.

BTW this question is from Kaplan for the SAT Maths.

 

[PeroK]

Are they asking us to find initial ration or final ration? According to the book solution, they found the final ration. But when I read it, I feel like they are asking for the initial ration.

BTW this question is from Kaplan for the SAT Maths.

Does it matter? Your solution is good. Move on.

 

[Kaushik]

Does it matter? You're solution is good. Move on.

The answer I got wasn't there in the options. So from what your saying, the book solution must be off.

 

[PeroK]

The answer I got wasn't there in the options. So from what your saying, the book solution must be off.

Looks that way.

 

[PeroK]

Suppose (at the beginning) Amal had 20 and Julia has 1.

Amal gives 10 to Geoffrey, leaving himself 10 and making Geoffrey up to 15 (to satify the 2:3 ratio). So, Geoffrey had 5 to begin with and now has 15. That's the 5:1 ratio with Julia (but before Geoffrey got Amal's fireworks!).

These word puzzles often end up like this. A hopeless muddle of words and confusion all round.