Izzy is making cookies. the recipe for 1/4 cup of butter and 3/8 cup of sugar. how much sugar would izzy use if she used 1 cup of butter? write your answer as a mixed number

To solve this equation, we have to set up a proportion, because we want to keep the ratio of butter to sugar equal between the two recipes.  Let x represent the amount of sugar that we are trying to find.

1/4 cup butter/3/8 cup sugar = 1 cup butter/ x cup sugar

To solve this proportion, we need to use cross products, or the multiplication of the numerator of one fraction by the denominator of the other, and setting them equal to one another.  If done properly, the resulting equation is:

1/4x= 3/8

Finally, we just need to divide both sides by 1/4, which is the coefficient of x, as we are trying to get x alone.  Your final answer is 

x=1.5.

Therefore, this means that if Izzy uses 1 cup of butter, she would use 1 1/2 cups of sugar.

1/4cup of butter3/8 cup of sugar
1 cup of butter   x
x=(1 cup of butter.(3/8) cup of sugar) / 1/4 cup of batter=12/8 cup of sugar.

12/8=(8+4)/8=8/8 + 4/8=1+1/2=1  1/2

Solution=1 1/2 cup of sugar.