Cathy bought some necklaces and rings for her friends. The price of each necklace was $4.40 while the price of each ring was $14.30. For every 7 rings bought, she was given one such necklace for free. After receiving the free necklaces, the number of necklaces was ¹₅ of the number of rings bought. If Cathy paid a total of $3565.10, how much more did she pay for the rings than the necklaces?

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

	Rings	Necklaces
	Bought	Free	Bought
Number	35 u	5 u	2 u
Value	$14.30	0	$4.40
Total value	500.5 u	0	8.8 u

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

Cost of the bought rings
= 35 u x 14.30
= 500.5 u

Cost of the bought necklaces
= 2 u x 4.40  
= 8.8 u

Total cost of the bought items
= 500.5 u + 8.8 u
= 509.3 u

509.3 u = 3565.10

1 u = 3565.10 ÷ 509.30 = 7

Amount that she paid more for the rings than the necklaces
= 500.5 u - 8.8 u 
= 491.7 u
= 491.7 x 7
= $3441.90

Answer(s): $3441.90