Usha spent $190 on some pens, pencils and files. The number of pens she bought was ²₃ the number of pencils. The number of files she bought was ¹₅ the number of pencils. The ratio of the amount of money she spent on the pens, pencils and files was 8 : 9 : 2. The pencils were sold at 5 for $6. Find the price of 1 pen.

Amount spent
Pens	Pencils	Files	Total
8 u	9 u	2 u	$190

Total amount that Usha spent on pens, pencils and files
= 8 u + 9 u + 2 u
= 19 u

19 u = 190

1 u = 190 ÷ 19 = 10

Amount that Usha spent on pencils
= 9 u
= 9 x 10
= $90

Number of sets of pencils of 5 bought
= 90 ÷ 6
= 15

Number of pencils that Usha bought
= 15 x 5
= 75

Number of items bought
Pens	Pencils	Files	Total
2x5	3x5
	5x3	1x3
10 p	15 p	3 p	28 p

The number of pencils bought is repeated.  Make the number of pencils bought is the same.  LCM of 3 and 5 is 15.

Number of pencils that Usha bought = 15 p

15 p = 75

1 p = 75 ÷ 15 = 5

Number of pens that Usha bought
= 10 p
= 10 x 5
= 50

Amount that Usha spent on pens
= 8 u
= 8 x 10
= $80

Price of 1 pen
= 80 ÷ 50
= $1.60

Answer(s): $1.60