Total value of all the notes : $130
There are 24 notes in total.
Same number of notes of the $2 and $10 kind.


Assumption method :

① Assume all 24 notes are $5 first.

Total value of 24 pieces of $5 notes
= 24 x $5
= $120


② $120 is too little.

We need to remove some $5 notes and replace them with $2 and $10.

Since there are equal number of $2 and $10 notes,

for each replacement, we have to remove two $5 notes and replace them with one $2 and one $10.

Decrease in total value after removing two $5 notes = $5 x 2 = $10

Increase in total value after adding one $2 and one $10 note = $2 + $10 = $12

Overall increase in total value for each replacement = $12 - $10 = $2


④ From $120 to the right value of $130, we need to increase the total value by $10.

($130 - $120 = $10)


Since each replacement increases the total value by $2,

Number of replacements needed

= $10 ÷ $2
= 5


5 replacements means we need 5 pieces of $2 notes to do the replacements.

This tells us that there are 5 pieces of $2 notes in the first place.

Checking :

So there are :

5 pieces of $2

5 pieces of $10

14 pieces of $5 (24 - 5 - 5 = 14)



Total value of the notes
= 5 x $2 + 5 x $10 + 14 x $5
= $10 + $50 + $70
= $130

(Matches the question information)

Working that you'll need to present :


① $10 + $2 = $12
② $5 x 2 = $10
③ $12 - $10 = $2
④ $5 x 24 = $120
⑤ $130 - $120 = $10
⑥$10 ÷ $2 = 5

Thank you very much