Answer:
Let's call the certain number "N."
According to the problem, 1/4 of N is added to 4 1/3, which can be represented as:
(1/4)N + 4 1/3
And this sum is equal to when 1/3 of N is subtracted from 20 2/3:
20 2/3 - (1/3)N
Now, we can set up an equation with these two expressions being equal:
(1/4)N + 4 1/3 = 20 2/3 - (1/3)N
First, let's convert all the mixed numbers to improper fractions:
4 1/3 = 13/3
20 2/3 = 62/3
Now, the equation becomes:
(1/4)N + 13/3 = 62/3 - (1/3)N
Next, we can simplify the equation by getting rid of fractions. Multiply both sides of the equation by 12 (the least common multiple of 4 and 3) to eliminate the fractions:
12 * [(1/4)N + 13/3] = 12 * [62/3 - (1/3)N]
3N + 52 = 248 - 4N
Now, let's isolate the N terms on one side and the constants on the other:
3N + 4N = 248 - 52
7N = 196
Now, divide both sides by 7 to solve for N:
N = 196 / 7
N = 28
So, the certain number is 28.