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The three most popular ice cream flavors are chocolate, strawberry, and vanilla, comprising 97% of the flavors sold at an ice cream shop. If vanilla sells 10% more than twice strawberry, and chocolate sells 7% more than vanilla, how much of the total ice cream consumption are the vanilla, chocolate, and strawberry flavors?

Respuesta :

Using a system of equations, it is found that:

  • 38% consumes vanilla.
  • 14% consumes strawberry.
  • 45% consumes chocolate.

In our system, we have that:

  • x is the percentage of vanilla.
  • y is the percentage of strawberry.
  • z is the percentage of chocolate.

Those 3 compromise 97% of the flavors, hence:

[tex]x + y + z = 97[/tex]

Vanilla sells 10% more than twice strawberry, hence:

[tex]x = 10 + 2y[/tex]

Chocolate sells 7% more than vanilla, hence:

[tex]z = x + 7[/tex]

Since [tex]x = 10 + 2y[/tex]

[tex]z = 10 + 2y + 7[/tex]

[tex]z = 2y + 17[/tex]

Replacing in the first equation, we can solve for y:

[tex]x + y + z = 97[/tex]

[tex]10 + 2y + y + 2y + 17 = 97[/tex]

[tex]5y = 70[/tex]

[tex]y = \frac{70}{5}[/tex]

[tex]y = 14[/tex]

With y, we can solve for x and for z.

[tex]x = 10 + 2y = 10 + 2(14) = 38[/tex]

[tex]y = 2y + 17 = 2(14) + 17 = 45[/tex]

Hence:

  • 38% consumes vanilla.
  • 14% consumes strawberry.
  • 45% consumes chocolate.

A similar problem is given at https://brainly.com/question/24778333

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