Question

There are 3 times as many males as females on the maths course at university. What fraction of the course are male?

Give your answer in its simplest form.
Colin gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many smarties as marshmallows. What proportion of the bag of sweets are cola bottles?
Give your answer in its simplest form

Answer 1

(1)

If there are three times as many males as females, the ratio of males to females would be 3:1.

To make this more clearer. Suppose you have 100 students. for each 4 students, 3 of them are male and 1 is a female.

We can then say there are 75 males and 25 females.

Expressing this as a ratio(fraction) is easy 3 out of 4 are males and 1 out of 4 are females. So the ratio of males would be;

`r(m) = (3)/(4)`

(2)

Let x be the number of cola bottles

Let y be the number of smarties

Let z be the number of marshmallows

x=3y (since there are 3 times more x than y)

y=2z (since there are 2 times more y than z)

we know that marshmallows are twice as less as smarties. so for 1 marshmallow you'd have 2 smarties. But we also know that cola bottles should be 2×3=6 since we have 3 times more cola bottles than smarties.

Adding up our total sweets we get;

1+2+6=9

But how many of those are cola bottles? 6!

So the ratio of cola bottles can be expressed as,

`r(c) = (6)/(9) = (2)/(3)`

You can simplify the numerator and denominator by 3 to get 2 over 3.