Elyse bought some necklaces and rings for her friends. The price of each necklace was $3.80 while the price of each ring was $11.60. For every 7 rings bought, she was given one such necklace for free. After receiving the free necklaces, the number of necklaces was ¹₄ of the number of rings bought. If Elyse paid a total of $2689.60, how much more did she pay for the rings than the necklaces?

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

	Rings	Necklaces
	Bought	Free	Bought
Number	28 u	4 u	3 u
Value	$11.60	0	$3.80
Total value	324.8 u	0	11.4 u

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

Cost of the bought rings
= 28 u x 11.60
= 324.8 u

Cost of the bought necklaces
= 3 u x 3.80  
= 11.4 u

Total cost of the bought items
= 324.8 u + 11.4 u
= 336.2 u

336.2 u = 2689.60

1 u = 2689.60 ÷ 336.20 = 8

Amount that she paid more for the rings than the necklaces
= 324.8 u - 11.4 u 
= 313.4 u
= 313.4 x 8
= $2507.20

Answer(s): $2507.20