Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
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]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
