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Fang travelled to Singapore and had $960 with her, all in $50 and $5 denominations. She walked up to a local and exchanged a piece of $50-note for several $5-notes. After the exchange, the number of $5-notes she had was twice the number of $50-notes. How many pieces of $50-notes did Fang have initially?

Question

Fang travelled to Singapore and had 960withher,allin960 with her, all in 50 and 5denominations.Shewalkeduptoalocalandexchangedapieceof5 denominations. She walked up to a local and exchanged a piece of 50-note for several 5−notes.Aftertheexchange,thenumberof5-notes. After the exchange, the number of 5-notes she had was twice the number of 50−notes.Howmanypiecesof50-notes. How many pieces of 50-notes did Fang have initially?

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Solution

Let's denote the number of 50notesasxandthenumberof50 notes as x and the number of 5 notes as y.

From the problem, we know that:

  1. The total amount of money is $960, so 50x + 5y = 960.
  2. Fang exchanged one 50noteforseveral50 note for several 5 notes, so she now has x-1 50notesandy+1050 notes and y+10 5 notes.
  3. After the exchange, the number of 5notesistwicethenumberof5 notes is twice the number of 50 notes, so y+10 = 2(x-1).

Now we can solve these equations step by step:

First, let's simplify the second equation: y+10 = 2x - 2, which simplifies to y = 2x - 12.

Next, substitute y = 2x - 12 into the first equation: 50x + 5(2x - 12) = 960, which simplifies to 60x - 60 = 960, and further simplifies to 60x = 1020.

Finally, solve for x: x = 1020 / 60 = 17.

So, Fang initially had 17 pieces of $50 notes.

This problem has been solved

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