Sarah opens a small bag of chocolate candies and notices that out of 210 candies, 63 are brown. She assumes the color breakdown is consistent over all sizes of packaging. When she opens a bulk package of the same candies with 4,800 pieces, how many brown candies should she expect?

1440

Step-by-step explanation:

We can solve this problem by applying the rule of three.

In fact, we know that:

- Over a package of 210 candies,

- The number of brown candies is 63

- Here we want to find what is the number of brown candies when the total number of candies contained in the package is 4800

So we can set up the following rule of three:

where

x = number of brown candies when the total number of candies contained in the package is 4800

Solving the expression for x, we find:

So, Sarah can expect to find 1440 brown candies in a package of 4800 pieces.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: