Question

A group of people went to a coffee shop.

Answer 1

Answer:

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 = $\frac{13}{45}$