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Sagot :
Answer:
Fraction of the people chose a tart = [tex]\frac{13}{45}[/tex]
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 = [tex]\frac{1}{5}.5x[/tex] = x
Total number of people who chooses tea = [tex]\frac{4}{5}.5x[/tex] = 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 = [tex]\frac{2}{9}x[/tex]
Total number of people who choose tart after coffee = [tex]\frac{7}{9}x[/tex]
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 = [tex]\frac{5}{6}.4x = \frac{20}{6}x[/tex]
Total number of people who choose tart after tea = [tex]\frac{1}{6}.4x = \frac{4}{6}x[/tex]
∴ 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 = [tex]\frac{7}{9}x[/tex] + [tex]\frac{4}{6}x[/tex]
= [tex]\frac{7}{9}x + \frac{2}{3}x[/tex]
= [tex]\frac{7x + 6x}{9}[/tex]
= [tex]\frac{13}{9}x[/tex]
⇒Total number of people who chooses tart = [tex]\frac{13}{9}x[/tex]
Now,
Fraction of the people chose a tart = [tex]\frac{People choose tart}{Total people}[/tex]
= [tex]\frac{\frac{13}{9}x }{5x}[/tex]
= [tex]\frac{13}{45}[/tex]
⇒Fraction of the people chose a tart = [tex]\frac{13}{45}[/tex]
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