Rachel bought some rings and necklaces for her friends. The price of each ring was $2.20 while the price of each necklace was $11.50. 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 Rachel paid a total of $2753.30, 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	$11.50	0	$2.20
Total value	241.5 u	0	8.8 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 11.50
= 241.5 u

Cost of the bought rings
= 4 u x 2.20  
= 8.8 u

Total cost of the bought items
= 241.5 u + 8.8 u
= 250.3 u

250.3 u = 2753.30

1 u = 2753.30 ÷ 250.30 = 11

Amount that she paid more for the necklaces than the rings
= 241.5 u - 8.8 u 
= 232.7 u
= 232.7 x 11
= $2559.70

Answer(s): $2559.70