Question

A group of people went to a coffee shop.

Each person chose a drink and a treat.


number of people who chose coffee: number of people who chose tea = 1:4


Of those who chose coffee,

number of people who chose a muffin number of people who chose a tart = 2:7


Of those who chose tea,

number of people who chose a muffin : number of people who chose a tart = 5:1


What fraction of the people chose a tart?

Answer 1

Fraction of the people chose a tart =
`(13)/(45)`

Explanation:

Given - A group of people went to a coffee shop. Each person chose a

drink and a treat. number of people who chose coffee: number of

people who chose tea = 1:4. Of those who chose coffee, number of

people who chose a muffin number of people who chose a tart =

2:7. Of those who chose tea, number of people who chose a muffin

: number of people who chose a tart = 5:1.

To find - What fraction of the people chose a tart?

Proof -

Let the Total number of People went to a coffee shop = 5x

Now,

As given, number of people who chose coffee: number of people who chose tea = 1:4

⇒Total number of people who chooses coffee =
`(1)/(5).5x` = x

Total number of people who chooses tea =
`(4)/(5).5x` = 4x

Now,

As given,

Of those who choose coffee, number of people who chose a muffin number of people who chose a tart = 2:7

⇒Total number of people who choose muffin after coffee =
`(2)/(9)x`

Total number of people who choose tart after coffee =
`(7)/(9)x`

Also,

Given that

Of those who chose tea, number of people who chose a muffin : number of people who chose a tart = 5:1

⇒Total number of people who choose muffin after tea =
`(5)/(6).4x = (20)/(6)x`

Total number of people who choose tart after tea =
`(1)/(6).4x = (4)/(6)x`

∴ we get

Total number of people who chooses tart = Total number of people who choose tart after coffee + Total number of people who choose tart after tea

⇒Total number of people who chooses tart =
`(7)/(9)x` +
`(4)/(6)x`

=
`(7)/(9)x + (2)/(3)x`

=
`(7x + 6x)/(9)`

=
`(13)/(9)x`

⇒Total number of people who chooses tart =
`(13)/(9)x`

Now,

Fraction of the people chose a tart =
`(People choose tart)/(Total people)`

=
`((13)/(9)x )/(5x)`

=
`(13)/(45)`

⇒Fraction of the people chose a tart =
`(13)/(45)`