Gwen spent $36 on some files, notebooks and pencils. The number of files she bought was ¹₂ the number of notebooks. The number of pencils she bought was ³₄ the number of notebooks. The ratio of the amount of money she spent on the files, notebooks and pencils was 9 : 7 : 2. The notebooks were sold at 4 for $7. Find the price of 1 file.

Amount spent
Files	Notebooks	Pencils	Total
9 u	7 u	2 u	$36

Total amount that Gwen spent on files, notebooks and pencils
= 9 u + 7 u + 2 u
= 18 u

18 u = 36

1 u = 36 ÷ 18 = 2

Amount that Gwen spent on notebooks
= 7 u
= 7 x 2
= $14

Number of sets of notebooks of 4 bought
= 14 ÷ 7
= 2

Number of notebooks that Gwen bought
= 2 x 4
= 8

Number of items bought
Files	Notebooks	Pencils	Total
1x2	2x2
	4x1	3x1
2 p	4 p	3 p	9 p

The number of notebooks bought is repeated.  Make the number of notebooks bought is the same.  LCM of 2 and 4 is 4.

Number of notebooks that Gwen bought = 4 p

4 p = 8

1 p = 8 ÷ 4 = 2

Number of files that Gwen bought
= 2 p
= 2 x 2
= 4

Amount that Gwen spent on files
= 9 u
= 9 x 2
= $18

Price of 1 file
= 18 ÷ 4
= $4.50

Answer(s): $4.50