There are 3 times as many females as males on the maths course at university. What fraction of the course are female? Give your answer in its simplest form. 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. He also picks twice as many marshmallows as smarties. What proportion of the bag of sweets are marshmallows? Give your answer in its simplest form.

1. The fraction of the female in the course is  

2. The fraction of the marshmallows in the bag is  

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)  

The ratio of females = females/total

∴ The fraction of the females in the course =

∴ The fraction of the female in the course is  

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 =

- Simplify it by divide up and down by 2

∴ The fraction of the marshmallows in the bag is