Helen spent $126 on a coat. She spent ²₁₁ of her remaining money on a sweater and a vest, after which half her money was left.

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

Coat	Remaining amount
	Sweater	Vest	Left
$126	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 coat
= ^Coat_Total 
= ⁷₁₈ 

(b)
Cost of the coat = 7 u

7 u = 126

1 u = 126 ÷ 7 = 18

Cost of the sweater and the vest
= 2 u
= 2 x 18
= $36

Cost of the vest = 1 p
Cost of the sweater = 5 p

Total cost of the vest and the sweater 
= 1 p + 5 p
= 6 p

6 p = 36

1 p = 36 ÷ 6 = 6

Amount that the sweater was more than the vest
= 5 p - 1 p
= 4 p
= 4 x 6
= $24

Answer(s): (a) ⁷₁₈; (b) $24