Gwen bought some necklaces and bracelets for her friends. The price of each necklace was $3.90 while the price of each bracelet was $14.20. For every 7 bracelets bought, she was given one such necklace for free. After receiving the free necklaces, the number of necklaces was ¹₄ of the number of bracelets bought. If Gwen paid a total of $3683.70, how much more did she pay for the bracelets than the necklaces?

Bracelets	Necklaces
4x7	1x7
Bought	Free	Bought
7x4	1x4
28 u	4 u	3 u

	Bracelets	Necklaces
	Bought	Free	Bought
Number	28 u	4 u	3 u
Value	$14.20	0	$3.90
Total value	397.6 u	0	11.7 u

The number of bracelets bought is the repeated identity. Make the number of bracelets bought the same.  LCM of 4 and 7 is 28.

Cost of the bought bracelets
= 28 u x 14.20
= 397.6 u

Cost of the bought necklaces
= 3 u x 3.90  
= 11.7 u

Total cost of the bought items
= 397.6 u + 11.7 u
= 409.3 u

409.3 u = 3683.70

1 u = 3683.70 ÷ 409.30 = 9

Amount that she paid more for the bracelets than the necklaces
= 397.6 u - 11.7 u 
= 385.9 u
= 385.9 x 9
= $3473.10

Answer(s): $3473.10