Helen spent $105 on a sweater. She spent ²₁₁ of her remaining money on a jacket and a shirt, after which half her money was left.

1. What fraction of her money did she spend on the sweater?
2. The cost of the shirt is ¹₅ the cost of the jacket. How much more does the jacket cost than the shirt?

Sweater	Remaining amount
	Jacket	Shirt	Left
$105	2		9
1x9			1x9
7 u	2 u		9 u

(a)
The amount of money left is repeated. Make the numerators the same LCM of 1 and 9 is 9. 

1x92x9 of total money = 911 of remaining amount
918 of total money = 911 of remaining amount

Fraction of her money that she spent on the sweater
= ^Sweater_Total 
= ⁷₁₈ 

(b)
Cost of the sweater = 7 u

7 u = 105

1 u = 105 ÷ 7 = 15

Cost of the jacket and the shirt
= 2 u
= 2 x 15
= $30

Cost of the shirt = 1 p
Cost of the jacket = 5 p

Total cost of the shirt and the jacket 
= 1 p + 5 p
= 6 p

6 p = 30

1 p = 30 ÷ 6 = 5

Amount that the jacket was more than the shirt
= 5 p - 1 p
= 4 p
= 4 x 5
= $20

Answer(s): (a) ⁷₁₈; (b) $20