Kesha's mean grade for the first two terms was 74. What grade must she get in the third term to get an exact passing average of 75?

To find out what grade Kesha must get in the third term to achieve an exact passing average of 75, we need to consider the weight of each term.

Let's assume the first term has a weight of x and the second term has a weight of y. Since we are interested in Kesha's average grade, we can set up an equation using her mean grade for the first two terms and the passing average.

The equation can be written as follows:

(x * 74 + y * 74 + z * g) / (x + y + z) = 75

Where:
x = weight of the first term
y = weight of the second term
z = weight of the third term
g = grade of the third term

Since we know that Kesha's mean grade for the first two terms is 74, we have:

x * 74 + y * 74 = 2 * 74

Simplifying this equation gives us:

74x + 74y = 148

Substituting this equation into the original equation, we have:

(148 + z * g) / (x + y + z) = 75

Now, we can solve for g, the grade Kesha must get in the third term, to achieve an average of 75.

(148 + z * g) = 75 * (x + y + z)

148 + z * g = 75x + 75y + 75z

Substituting the value of (75x + 75y) from the previous equation, we have:

148 + z * g = 148 + 75z

Simplifying further, we get:

z * g = 75z

Dividing both sides of the equation by z gives us:

g = 75

Therefore, Kesha must obtain a grade of 75 in the third term to achieve an exact passing average of 75.