Esther spent $80 on some pencils, files and notebooks. The number of pencils she bought was ¹₄ the number of files. The number of notebooks she bought was ³₅ the number of files. The ratio of the amount of money she spent on the pencils, files and notebooks was 4 : 5 : 1. The files were sold at 4 for $8. Find the price of 1 pencil.

Amount spent
Pencils	Files	Notebooks	Total
4 u	5 u	1 u	$80

Total amount that Esther spent on pencils, files and notebooks
= 4 u + 5 u + 1 u
= 10 u

10 u = 80

1 u = 80 ÷ 10 = 8

Amount that Esther spent on files
= 5 u
= 5 x 8
= $40

Number of sets of files of 4 bought
= 40 ÷ 8
= 5

Number of files that Esther bought
= 5 x 4
= 20

Number of items bought
Pencils	Files	Notebooks	Total
1x5	4x5
	5x4	3x4
5 p	20 p	12 p	37 p

The number of files bought is repeated.  Make the number of files bought is the same.  LCM of 4 and 5 is 20.

Number of files that Esther bought = 20 p

20 p = 20

1 p = 20 ÷ 20 = 1

Number of pencils that Esther bought
= 5 p
= 5 x 1
= 5

Amount that Esther spent on pencils
= 4 u
= 4 x 8
= $32

Price of 1 pencil
= 32 ÷ 5
= $6.40

Answer(s): $6.40