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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?

User RedPixel
by
3.7k points

1 Answer

10 votes

Answer:

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)

User Cvibha
by
4.2k points