Answer:
Therefore, the value of x is 8. This means that if we have 6 cups of flour, we can make 8 dozens of cookies.
Explanation:
The value of x is 8. This means that if we have 6 cups of flour, we can make 8 dozen of cookies.
To solve this problem, we can use the concept of proportions. In a proportional relationship, the ratios between the corresponding values of two sets of numbers are equal.
In this case, the relationship between the cups of flour and the number of cookies is proportional. We can set up a proportion by comparing the ratios of flour to cookies.
The first ratio is 3 cups of flour to 4 dozen of cookies, which can be written as 3/4.
The second ratio is 6 cups of flour to x dozens of cookies, which can be written as 6/x.
The third ratio is 12 cups of flour to 16 dozen of cookies, which can be written as 12/16.
Now, we can set up the proportion:
3/4 = 6/x = 12/16
To solve for x, we can cross-multiply and then solve the resulting equation.
(3)(x) = (6)(4)
3x = 24
x = 24/3
x = 8
Therefore, the value of x is 8. This means that if we have 6 cups of flour, we can make 8 dozens of cookies.