Erika bought some rings and necklaces for her friends. The price of each ring was $2.50 while the price of each necklace was $10.40. For every 7 necklaces bought, she was given one such ring for free. After receiving the free rings, the number of rings was ¹₄ of the number of necklaces bought. If Erika paid a total of $2688.30, how much more did she pay for the necklaces than the rings?

Necklaces	Rings
4x7	1x7
Bought	Free	Bought
7x4	1x4
28 u	4 u	3 u

	Necklaces	Rings
	Bought	Free	Bought
Number	28 u	4 u	3 u
Value	$10.40	0	$2.50
Total value	291.2 u	0	7.5 u

The number of necklaces bought is the repeated identity. Make the number of necklaces bought the same.  LCM of 4 and 7 is 28.

Cost of the bought necklaces
= 28 u x 10.40
= 291.2 u

Cost of the bought rings
= 3 u x 2.50  
= 7.5 u

Total cost of the bought items
= 291.2 u + 7.5 u
= 298.7 u

298.7 u = 2688.30

1 u = 2688.30 ÷ 298.70 = 9

Amount that she paid more for the necklaces than the rings
= 291.2 u - 7.5 u 
= 283.7 u
= 283.7 x 9
= $2553.30

Answer(s): $2553.30