Mathematics, 02.03.2021 03:10 letsgetcookingblog

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?

Answers: 1

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Answer from: sudotoxic

Fraction of the people chose a tart = $\frac{13}{45}$

Step-by-step 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 = $\frac{1}{5}.5x$ = x

Total number of people who chooses tea = $\frac{4}{5}.5x$ = 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 = $\frac{2}{9}x$

Total number of people who choose tart after coffee = $\frac{7}{9}x$

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 = $\frac{5}{6}.4x = \frac{20}{6}x$

Total number of people who choose tart after tea = $\frac{1}{6}.4x = \frac{4}{6}x$

∴ 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 = $\frac{7}{9}x$ + $\frac{4}{6}x$

= $\frac{7}{9}x + \frac{2}{3}x$

= $\frac{7x + 6x}{9}$

= $\frac{13}{9}x$

⇒Total number of people who chooses tart = $\frac{13}{9}x$

Now,

Fraction of the people chose a tart = $\frac{People choose tart}{Total people}$

= $\frac{\frac{13}{9}x }{5x}$

= $\frac{13}{45}$

⇒Fraction of the people chose a tart = $\frac{13}{45}$

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