Question

A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flour you use. Write a direct variation equation to represent this.

Answer 1

A direct variation equation to represent this ;
`y = (2)/(3)x`

Explanation:

Direct Variation states that a relationship between two variables in which one is a constant multiple of the other one.

In other words, when one of the variable changes then the other changes in proportion to the first.

If b is directly proportional to a, then the equation is in the i.e,

form
`b = ka` where k is the constant of variation.

Let y represents the number of muffins and x represents the amount of flour.

It is given that the number of muffins varies directly with the amount of flour you use.

As per the given statement:

y = 2 dozen corn and x = 3 cups of flour.

Then, by definition of Direct variation;

y = kx

Substitute the given values to find k;

`2 = 3k`

Divide both sides by 3 we get;

`k = (2)/(3)`

then, equation is,
`y = (2)/(3)x`

Therefore, a direct variation equation to represent this situation is;
`y = (2)/(3)x`