Helen spent $100 on a coat. She spent ³₁₁ of her remaining money on a sweater and a jumpsuit, after which half her money was left.

1. What fraction of her money did she spend on the coat?
2. The cost of the jumpsuit is ¹₃ the cost of the sweater. How much more does the sweater cost than the jumpsuit?

Coat	Remaining amount
	Sweater	Jumpsuit	Left
$100	3		8
1x8			1x8
5 u	3 u		8 u

(a)
The amount of money left is repeated. Make the numerators the same LCM of 1 and 8 is 8. 

1x82x8 of total money = 811 of remaining amount
816 of total money = 811 of remaining amount

Fraction of her money that she spent on the coat
= ^Coat_Total 
= ⁵₁₆ 

(b)
Cost of the coat = 5 u

5 u = 100

1 u = 100 ÷ 5 = 20

Cost of the sweater and the jumpsuit
= 3 u
= 3 x 20
= $60

Cost of the jumpsuit = 1 p
Cost of the sweater = 3 p

Total cost of the jumpsuit and the sweater 
= 1 p + 3 p
= 4 p

4 p = 60

1 p = 60 ÷ 4 = 15

Amount that the sweater was more than the jumpsuit
= 3 p - 1 p
= 2 p
= 2 x 15
= $30

Answer(s): (a) ⁵₁₆; (b) $30