Lynn bought some rings and necklaces for her friends. The price of each ring was $4.10 while the price of each necklace was $10.70. For every 7 necklaces bought, she was given one such ring for free. After receiving the free rings, the number of rings was ¹₅ of the number of necklaces bought. If Lynn paid a total of $3444.30, how much more did she pay for the necklaces than the rings?

Necklaces	Rings
5x7	1x7
Bought	Free	Bought
7x5	1x5
35 u	5 u	2 u

	Necklaces	Rings
	Bought	Free	Bought
Number	35 u	5 u	2 u
Value	$10.70	0	$4.10
Total value	374.5 u	0	8.2 u

The number of necklaces bought is the repeated identity. Make the number of necklaces bought the same.  LCM of 5 and 7 is 35.

Cost of the bought necklaces
= 35 u x 10.70
= 374.5 u

Cost of the bought rings
= 2 u x 4.10  
= 8.2 u

Total cost of the bought items
= 374.5 u + 8.2 u
= 382.7 u

382.7 u = 3444.30

1 u = 3444.30 ÷ 382.70 = 9

Amount that she paid more for the necklaces than the rings
= 374.5 u - 8.2 u 
= 366.3 u
= 366.3 x 9
= $3296.70

Answer(s): $3296.70