Hazel bought some rings and necklaces for her friends. The price of each ring was $2.30 while the price of each necklace was $13.70. 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 Hazel paid a total of $2078.30, 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	$13.70	0	$2.30
Total value	287.7 u	0	9.2 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 13.70
= 287.7 u

Cost of the bought rings
= 4 u x 2.30  
= 9.2 u

Total cost of the bought items
= 287.7 u + 9.2 u
= 296.9 u

296.9 u = 2078.30

1 u = 2078.30 ÷ 296.90 = 7

Amount that she paid more for the necklaces than the rings
= 287.7 u - 9.2 u 
= 278.5 u
= 278.5 x 7
= $1949.50

Answer(s): $1949.50