Sarah bought some rings and necklaces for her friends. The price of each ring was $3.20 while the price of each necklace was $10.90. For every 7 necklaces bought, she was given one such ring for free. After receiving the free rings, the number of rings was ¹₃ of the number of necklaces bought. If Sarah paid a total of $2658.70, how much more did she pay for the necklaces than the rings?

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

	Necklaces	Rings
	Bought	Free	Bought
Number	21 u	3 u	4 u
Value	$10.90	0	$3.20
Total value	228.9 u	0	12.8 u

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

Cost of the bought necklaces
= 21 u x 10.90
= 228.9 u

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

Total cost of the bought items
= 228.9 u + 12.8 u
= 241.7 u

241.7 u = 2658.70

1 u = 2658.70 ÷ 241.70 = 11

Amount that she paid more for the necklaces than the rings
= 228.9 u - 12.8 u 
= 216.1 u
= 216.1 x 11
= $2377.10

Answer(s): $2377.10