Gem bought some bracelets and necklaces for her friends. The price of each bracelet was $3.50 while the price of each necklace was $10.90. For every 7 necklaces bought, she was given one such bracelet for free. After receiving the free bracelets, the number of bracelets was ¹₄ of the number of necklaces bought. If Gem paid a total of $2209.90, how much more did she pay for the necklaces than the bracelets?

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

	Necklaces	Bracelets
	Bought	Free	Bought
Number	28 u	4 u	3 u
Value	$10.90	0	$3.50
Total value	305.2 u	0	10.5 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 10.90
= 305.2 u

Cost of the bought bracelets
= 3 u x 3.50  
= 10.5 u

Total cost of the bought items
= 305.2 u + 10.5 u
= 315.7 u

315.7 u = 2209.90

1 u = 2209.90 ÷ 315.70 = 7

Amount that she paid more for the necklaces than the bracelets
= 305.2 u - 10.5 u 
= 294.7 u
= 294.7 x 7
= $2062.90

Answer(s): $2062.90