Since the ratio of the VALUE of the notes is 7 : 4, meaning $7 worth of $2 to $4 worth of $10 notes. Since this is impossible as you cant make $ odd numbers out of $2 notes and $4 out of $10 notes.

Clue: Think about how you can fulfill the criteria above.

Another way is to first pretend that the $2 notes are also $10 notes.


Since the ratio of the value is 7 : 4, and we treat the notes as the same kind for each set,

For every 7 $10 notes in one set, the other set has 4 $10 notes.

Now we know that the 7 $10 notes are actually made out of $2 notes instead.
So we find the value and then try to find the actual number of $2 notes that make up that value.


Value = 7 x $10 = $70

Since each note is $2 actually,
$70 ÷ $2 = 35

So for every 35 $2 notes, there are 4 $10 notes.


Ratio = 35 : 4
This is the simplest ratio already.

Least number of $2 notes is therefore 35

Or , simply recognise that $10 ÷ $2 = 5

5 $2 notes have the same value as 1 $10 note.

For the ratio of the value 7 : 4, see it as 7 $10 notes' worth to 4 $10 notes' worth.

Since you need 5 $2 notes to equal the value of 1 $10 note,

You need 7 x 5 $2 notes = 35 $2 notes ,
to equal the value that 7 $10 notes.

So the ratio is actually 35 : 4

Actual working is 3 steps only

$10 ÷ $2 = 5
7 x 5 = 35
Ratio = 35 : 4