# MatheMusic Puzzle - Solution

### The Puzzle:

Hungry Horace went into the Music Shop to buy some musical sweets which they were selling.

There were three special packs on offer:

1) Ten quavers and five crotchets: 35c (save 5c)

2) Ten crotchets and ten minims: $1 (save 20c)

3) Thirty quavers: 50c (save 10c)

What would be the full price of one quaver, one crotchet and one minim?

There were three special packs on offer:

1) Ten quavers and five crotchets: 35c (save 5c)

2) Ten crotchets and ten minims: $1 (save 20c)

3) Thirty quavers: 50c (save 10c)

What would be the full price of one quaver, one crotchet and one minim?

### Our Solution:

Thirty quavers normally cost 60c.

So quavers are 2c each.

"Ten quavers and five crotchets" is then "20c and five crotchets".

If this is normally 40c then five crotchets must normally cost 20c.

So crotchets are 4c each.

Similarly "Ten crotchets and ten minims" is "40c and ten minims".

If this normally costs $1.20 then ten minims must normally cost 80c.

So minims are 8c each.

The total full price of one quaver, one crotchet and one minim is then 2 + 4 + 8 = 14c

(Note: minim, crotchet, quaver are half, quarter and eighth notes in music)

So quavers are 2c each.

"Ten quavers and five crotchets" is then "20c and five crotchets".

If this is normally 40c then five crotchets must normally cost 20c.

So crotchets are 4c each.

Similarly "Ten crotchets and ten minims" is "40c and ten minims".

If this normally costs $1.20 then ten minims must normally cost 80c.

So minims are 8c each.

The total full price of one quaver, one crotchet and one minim is then 2 + 4 + 8 = 14c

(Note: minim, crotchet, quaver are half, quarter and eighth notes in music)

Puzzle Author: Stephen Froggatt

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