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viva [34]
3 years ago
13

If the gardener can fill the border with 30 flowers planted 12 inches apart, how far apart should the gardener plant 36 flowers

instead?
Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

10 inches

Step-by-step explanation:

This inversely proportional function, the more flowers - the less distance.

Flowers = k/distance

30 = k/12

k = 30*12 = 360

Flowers = 360/distance

New number of flowers and new distance:

Flowers = 360/distance

36 = 360/distance

distance = 360/36= 10 (inches)

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A group of people went to a coffee shop.
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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}

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