If Earl made a 1/2 pan of brownies using 2/3 cup of sugar, we can use a proportion to find out how much sugar he will need for a whole pan of brownies.
Let's call the amount of sugar needed for a whole pan of brownies "x". Since a whole pan is twice the size of a half pan, we can set up the proportion:
1/2 pan / 2/3 cup sugar = 1 whole pan / x cups sugar
To solve for x, we can cross-multiply and simplify:
1/2 pan * x cups sugar = 2/3 cup sugar * 1 whole pan
x/2 = 2/3
x = (2/3) * 2
x = 4/3
Therefore, Earl will need 4/3 cups of sugar for a whole pan of brownies. This can be simplified to 1 and 1/3 cups of sugar