Gem spent $102 on some pens, staplers and files. The number of pens she bought was ²₃ the number of staplers. The number of files she bought was ³₄ the number of staplers. The ratio of the amount of money she spent on the pens, staplers and files was 9 : 6 : 2. The staplers were sold at 2 for $6. Find the price of 1 pen.

Amount spent
Pens	Staplers	Files	Total
9 u	6 u	2 u	$102

Total amount that Gem spent on pens, staplers and files
= 9 u + 6 u + 2 u
= 17 u

17 u = 102

1 u = 102 ÷ 17 = 6

Amount that Gem spent on staplers
= 6 u
= 6 x 6
= $36

Number of sets of staplers of 2 bought
= 36 ÷ 6
= 6

Number of staplers that Gem bought
= 6 x 2
= 12

Number of items bought
Pens	Staplers	Files	Total
2x4	3x4
	4x3	3x3
8 p	12 p	9 p	29 p

The number of staplers bought is repeated.  Make the number of staplers bought is the same.  LCM of 3 and 4 is 12.

Number of staplers that Gem bought = 12 p

12 p = 12

1 p = 12 ÷ 12 = 1

Number of pens that Gem bought
= 8 p
= 8 x 1
= 8

Amount that Gem spent on pens
= 9 u
= 9 x 6
= $54

Price of 1 pen
= 54 ÷ 8
= $6.75

Answer(s): $6.75