Gwen bought some rings and necklaces for her friends. The price of each ring was $3.40 while the price of each necklace was $14.70. 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 Gwen paid a total of $1289.20, 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	$14.70	0	$3.40
Total value	308.7 u	0	13.6 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 14.70
= 308.7 u

Cost of the bought rings
= 4 u x 3.40  
= 13.6 u

Total cost of the bought items
= 308.7 u + 13.6 u
= 322.3 u

322.3 u = 1289.20

1 u = 1289.20 ÷ 322.30 = 4

Amount that she paid more for the necklaces than the rings
= 308.7 u - 13.6 u 
= 295.1 u
= 295.1 x 4
= $1180.40

Answer(s): $1180.40