Answer:
1. The fraction of the female in the course is  [tex]\frac{3}{4}[/tex]
2. The fraction of the marshmallows in the bag is  [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
We will use the ratio method to solve theses problems
1.
There are 3 times as many females as males on the mathematics course at university
That means the number of females is 3 times the number of males
Assume that x represent the fraction of females and y represents the fraction of the males in the course
By using the ratio method
→  female  : male  :  total
→  3      :  1     :  4 (3 + 1 = 4) Â
The ratio of females = females/total
∴ The fraction of the females in the course = [tex]\frac{3}{4}[/tex]
∴ The fraction of the female in the course is  [tex]\frac{3}{4}[/tex]
2.
Henry gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet
∵ He picks 3 times as many smarties as cola bottles
- That means the number of smarties is 3 times the number of
  cola bottles
∵ He also picks twice as many marshmallows as smarties
- That means the number of marshmallows is 2 times the number
  of smarties
By using the ratio method
→  Cola  :  smarties  :  marshmallows
→  1     :  3
→       :  1        :  2 ⇒ × 3
Multiply the second row by 3 to make the number of smarties in the two line equal
→       :  3        :  6
Write the ratio of the three types together
→  Cola  :  smarties  :  marshmallows  :  total
→  1     :  3        :  6             :  10 (1 + 3 + 6 = 10)
The ratio of marshmallows = marshmallows/total
∴ The fraction of the marshmallows in the bag = [tex]\frac{6}{10}[/tex]
- Simplify it by divide up and down by 2
∴ The fraction of the marshmallows in the bag is  [tex]\frac{3}{5}[/tex]
