Diana bought some rings and bracelets for her friends. The price of each ring was $4.50 while the price of each bracelet was $10.70. For every 8 bracelets bought, she was given one such ring for free. After receiving the free rings, the number of rings was ¹₃ of the number of bracelets bought. If Diana paid a total of $1675.80, how much more did she pay for the bracelets than the rings?

Bracelets	Rings
3x8	1x8
Bought	Free	Bought
8x3	1x3
24 u	3 u	5 u

	Bracelets	Rings
	Bought	Free	Bought
Number	24 u	3 u	5 u
Value	$10.70	0	$4.50
Total value	256.8 u	0	22.5 u

The number of bracelets bought is the repeated identity. Make the number of bracelets bought the same.  LCM of 3 and 8 is 24.

Cost of the bought bracelets
= 24 u x 10.70
= 256.8 u

Cost of the bought rings
= 5 u x 4.50  
= 22.5 u

Total cost of the bought items
= 256.8 u + 22.5 u
= 279.3 u

279.3 u = 1675.80

1 u = 1675.80 ÷ 279.30 = 6

Amount that she paid more for the bracelets than the rings
= 256.8 u - 22.5 u 
= 234.3 u
= 234.3 x 6
= $1405.80

Answer(s): $1405.80