Xylia bought some bracelets and necklaces for her friends. The price of each bracelet was $3.80 while the price of each necklace was $11.70. For every 5 necklaces bought, she was given one such bracelet for free. After receiving the free bracelets, the number of bracelets was ¹₃ of the number of necklaces bought. If Xylia paid a total of $732.40, how much more did she pay for the necklaces than the bracelets?

Necklaces	Bracelets
3x5	1x5
Bought	Free	Bought
5x3	1x3
15 u	3 u	2 u

	Necklaces	Bracelets
	Bought	Free	Bought
Number	15 u	3 u	2 u
Value	$11.70	0	$3.80
Total value	175.5 u	0	7.6 u

The number of necklaces bought is the repeated identity. Make the number of necklaces bought the same.  LCM of 3 and 5 is 15.

Cost of the bought necklaces
= 15 u x 11.70
= 175.5 u

Cost of the bought bracelets
= 2 u x 3.80  
= 7.6 u

Total cost of the bought items
= 175.5 u + 7.6 u
= 183.1 u

183.1 u = 732.40

1 u = 732.40 ÷ 183.10 = 4

Amount that she paid more for the necklaces than the bracelets
= 175.5 u - 7.6 u 
= 167.9 u
= 167.9 x 4
= $671.60

Answer(s): $671.60