SOLUTION:
Let x be the grade Christine should have for the fourth quarter.
It is given that her grades for the first three quarters are 88, 91, and 90 and she targets to have an average grade of not less than 92 in the four quarters.
Solving for x,
[tex] \begin{aligned} \dfrac{88 + 91 + 90 + x}{4} &\geq 92 \\ \\ \dfrac{269 + x}{4} &\geq 92 \\ \\ 4\cdot \dfrac{269 + x}{4} &\geq 4(92) \\ \\ 269 + x &\geq 368 \\ \\ x &\geq 368 - 269 \\ \\ x &\geq 99 \end{aligned} [/tex]
[tex] \therefore [/tex] Christine should have a grade of atleast 99 for the fourth quarter.
