Usha spent $66 on some pencils, files and pens. The number of pencils she bought was ¹₅ the number of files. The number of pens she bought was ¹₂ the number of files. The ratio of the amount of money she spent on the pencils, files and pens was 2 : 8 : 1. The files were sold at 5 for $6. Find the price of 1 pencil.

Amount spent
Pencils	Files	Pens	Total
2 u	8 u	1 u	$66

Total amount that Usha spent on pencils, files and pens
= 2 u + 8 u + 1 u
= 11 u

11 u = 66

1 u = 66 ÷ 11 = 6

Amount that Usha spent on files
= 8 u
= 8 x 6
= $48

Number of sets of files of 5 bought
= 48 ÷ 6
= 8

Number of files that Usha bought
= 8 x 5
= 40

Number of items bought
Pencils	Files	Pens	Total
1x2	5x2
	2x5	1x5
2 p	10 p	5 p	17 p

The number of files bought is repeated.  Make the number of files bought is the same.  LCM of 5 and 2 is 10.

Number of files that Usha bought = 10 p

10 p = 40

1 p = 40 ÷ 10 = 4

Number of pencils that Usha bought
= 2 p
= 2 x 4
= 8

Amount that Usha spent on pencils
= 2 u
= 2 x 6
= $12

Price of 1 pencil
= 12 ÷ 8
= $1.50

Answer(s): $1.50