Emma bought some necklaces and bracelets for her friends. The price of each necklace was $3.20 while the price of each bracelet was $12.40. For every 7 bracelets bought, she was given one such necklace for free. After receiving the free necklaces, the number of necklaces was ¹₃ of the number of bracelets bought. If Emma paid a total of $3005.20, how much more did she pay for the bracelets than the necklaces?

Bracelets	Necklaces
3x7	1x7
Bought	Free	Bought
7x3	1x3
21 u	3 u	4 u

	Bracelets	Necklaces
	Bought	Free	Bought
Number	21 u	3 u	4 u
Value	$12.40	0	$3.20
Total value	260.4 u	0	12.8 u

The number of bracelets bought is the repeated identity. Make the number of bracelets bought the same.  LCM of 3 and 7 is 21.

Cost of the bought bracelets
= 21 u x 12.40
= 260.4 u

Cost of the bought necklaces
= 4 u x 3.20  
= 12.8 u

Total cost of the bought items
= 260.4 u + 12.8 u
= 273.2 u

273.2 u = 3005.20

1 u = 3005.20 ÷ 273.20 = 11

Amount that she paid more for the bracelets than the necklaces
= 260.4 u - 12.8 u 
= 247.6 u
= 247.6 x 11
= $2723.60

Answer(s): $2723.60