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primary 5 | Maths
| Percentage

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20% of the notes are $10 notes.

40% of the remainder are $5 notes. Be careful because the word remainder is used here.

The rest are $2 notes.

The total value of the notes is $1026.

Let there be 100 units of notes (because I see a percent, I use 100 units).

20 units are $10 notes, since 20% of 100 units is equal to 20 units (which is why I used 100 units)

There are 80 units left at this point. 40% of these 80 units are $5 notes.

So 32 units are $5 notes and 48 units are $2 notes.

20 units are $10 notes.

32 units are $5 notes.

48 units are $2 notes.

I will label the total value of the notes as unit-notes.

The total value of the $10 notes is 20 x 10 = 200 unit-notes.

The total value of the $5 notes is 32 x 5 = 160 unit-notes.

The total value of the $2 notes is 48 x 2 = 96 unit-notes.

These add up to 456 unit-notes, which is numerically $1026 in value.

456 unit-notes = $1026

1 unit-note = 1026/456 = $2.25

Now we can work out the rest.

200 unit-notes = 200 x 2.25 = $450

160 unit-notes = 160 x 2.25 = $360

96 unit-notes = 96 x 2.25 = $216

Total value of $10 notes is $450.

Total value of $5 notes is $360.

Total value of $2 notes is $216.

Number of $10 notes = 450/10 = 45

Number of $5 notes = 360/5 = 72

Number of $2 notes = 216/2 = 108

Total number of notes

= 45 + 72 + 108

= 225

Total units = 100 x 2.25 = 225

I was going on the 2.25 route initially but decided to simplify the ratio since some students dislike decimals and will attempt to round down without realising the number of notes will end up being a whole number

### See 2 Answers

Remainder : 100% - 20% = 80% of total

5 dollar notes are 40% of remainder.

40% is 40/100 and 40/100 = 2/5

So $5 notes are 2/5 of remainder.

2/5 of remainder = 2/5 x 80% of total = 32% of total

$2 notes = 100% - 32% - 20% = 48% of total

Ratio of $10 notes : $5 notes : $2 notes = 20 : 32 : 48

= 5 : 8 : 12

Based on the info above, we can group 12 $2 notes, 5 $10 notes and 8 $5 notes into 1 set. 5 + 8 + 12 = 25, so there are 25 notes in a set.

Value of notes in 1 set

= $2 x 12 + $10 x 5 + $5 x 8

= $24 + $50 + $40

= $114

Since there's a total of $1026, number of sets = $1026 ÷ $114 = 9

Total number of notes = 9 sets x 25 per set = 225

J is an experienced tutor in this field.

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