# Question

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

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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