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Jamie and Karen shared $720. The ratio of the amount Jamie received to the amount that Karen received was 1:5.

Jamie received only $2 notes while Karen received only $5 notes.

Karen took some of her $5 notes and exchanged them for $2 notes of the same value with Jamie.

After the exchange, the ratio of the number of Jamie’s notes to that of the number of Karen’s notes became 1:3.

How many $5 notes did Karen use to exchange for $2 notes with Jamie?


J:K -> 1:5

That means J has $120, K has $600

Since J has all $2 notes, and K has all $5 notes

J has 60 pcs of $2 notes, K has 120 pcs of $5 notes for a total of 180 pcs of notes.

In the end, J:K (no. of notes) -> 1:3;

J has 45 pcs of notes, K has 135 pcs of notes, a difference of 15 pcs of notes

For K to exchange $5 notes to equal value of $2 notes, she must exchange in multiples of $10 (2pcs of $5 notes)

For every 2 pcs of $5 notes K gave to J, K received 5 pcs of $2 notes in return, meaning an increase of 3 pcs of notes per exchange of $10.

Since K had 15 more pcs of notes after the exchange, they had made 15 / 3 = 5 exchanges of $10 for a total of $50.

Therefore, Karen used $50 / $5 = 10 pcs of $5 notes for the exchange

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