Arecipe calls for 1 1/2 cups of sugar for a 3 pound cake. how many cups of sugar should be used for a 5 pound cake?

7 1/2 cups

Step-by-step explanation:

Write and solve an equation of ratios to answer this question:

Sugar          Cake weight

1 1/2 cups            3 lb

 =  

      x                     5 lb

Then, after cross-multiplying, we get:

3x = (3/2)(5), or 3x = 15/2, or x = 7/2

A 5 lb cake requires 7/2 (or 7 1/2) cups of sugar.

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: