Helen spent $51 on a sweater. She spent ⁴₁₁ of her remaining money on a jacket and a vest, after which half her money was left.

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

Sweater	Remaining amount
	Jacket	Vest	Left
$51	4		7
1x7			1x7
3 u	4 u		7 u

(a)
The amount of money left is repeated. Make the numerators the same LCM of 1 and 7 is 7. 

1x72x7 of total money = 711 of remaining amount
714 of total money = 711 of remaining amount

Fraction of her money that she spent on the sweater
= ^Sweater_Total 
= ³₁₄ 

(b)
Cost of the sweater = 3 u

3 u = 51

1 u = 51 ÷ 3 = 17

Cost of the jacket and the vest
= 4 u
= 4 x 17
= $68

Cost of the vest = 1 p
Cost of the jacket = 3 p

Total cost of the vest and the jacket 
= 1 p + 3 p
= 4 p

4 p = 68

1 p = 68 ÷ 4 = 17

Amount that the jacket was more than the vest
= 3 p - 1 p
= 2 p
= 2 x 17
= $34

Answer(s): (a) ³₁₄; (b) $34