#### Answer

The solution set is {t|t $\gt$ 300} , or (300, $\infty$) in interval notation.

#### Work Step by Step

We use the properties of inequalities to solve this inequality.
0.09t + 0.1(t + 200) $\gt$ 77
Use the distributive property.
0.09t + 0.1t + 20 $\gt$ 77
0.19t $\gt$ 57
Divide both sides by 0.19 to obtain:
t $\gt$ 300
The solution set is {t|t $\gt$ 300} , or (300, $\infty$) in interval notation.