Answer :
The question presents a direct variation problem. 'a' is the number of cookies per cup of flour, in this case '8'. 'y' is the number of cookies, 6 dozen in this case. 'x' is the cups of flour, in this case, 9 cups.
In the context of this question, the equation y = ax is a linear equation that models the relationship between the number of cookies (y) and the cups of flour (x). Here, 'a' is the constant of variation or, in context, the coefficient that expresses the number of cookies produced per cup of flour.
From the given problem, 2 dozen cookies are made with 3 cups of flour. This leads to the value of 'a' as 2 dozens (or 24 cookies) divided by 3 cups, which equals 8 cookies per cup.
Therefore, the equation illustrating the cookie-flour relationship is y = 8x.
To find the amount of flour for 6 dozens cookies, replace y with 6 dozens (or 72 cookies) in our equation.
Solve for x:
[tex]72 = 8x[/tex]
⇒[tex]x = \frac {72}{8}[/tex]
⇒[tex]x= 9[/tex].
Thus, 9 cups of flour are needed for 6 dozens cookies.
Learn more about direct variation here:
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