Question

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?

Answer 1

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:

$x + y + z = 97$

Vanilla sells 10% more than twice strawberry, hence:

$x = 10 + 2y$

Chocolate sells 7% more than vanilla, hence:

$z = x + 7$

Since $x = 10 + 2y$

$z = 10 + 2y + 7$

$z = 2y + 17$

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

$x + y + z = 97$

$10 + 2y + y + 2y + 17 = 97$

$5y = 70$

$y = \frac{70}{5}$

$y = 14$

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

$x = 10 + 2y = 10 + 2(14) = 38$

$y = 2y + 17 = 2(14) + 17 = 45$

Hence:

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

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