Yen bought some necklaces and bracelets for her friends. The price of each necklace was $3.80 while the price of each bracelet was $14.10. For every 5 bracelets bought, she was given one such necklace for free. After receiving the free necklaces, the number of necklaces was ¹₃ of the number of bracelets bought. If Yen paid a total of $1971.90, how much more did she pay for the bracelets than the necklaces?

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

	Bracelets	Necklaces
	Bought	Free	Bought
Number	15 u	3 u	2 u
Value	$14.10	0	$3.80
Total value	211.5 u	0	7.6 u

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

Cost of the bought bracelets
= 15 u x 14.10
= 211.5 u

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

Total cost of the bought items
= 211.5 u + 7.6 u
= 219.1 u

219.1 u = 1971.90

1 u = 1971.90 ÷ 219.10 = 9

Amount that she paid more for the bracelets than the necklaces
= 211.5 u - 7.6 u 
= 203.9 u
= 203.9 x 9
= $1835.10

Answer(s): $1835.10