Question 101919
Write down what you know. 
1.{{{(T1 + T2 + T3)/3=91}}} Colin's average from first three tests. 
2.{{{(T1+T2+T3+T4+T5+T6)/6=94}}} Colin's average from first three and last three tests must equal at least 94. 
3.{{{(T4 + T5 + T6)/3=x}}} Here's the unknown you need to find. It's Colin's average for the last three tests. Call it x. 
From equation 1, 
{{{(T1 + T2 + T3)/3=91}}}
{{{cross(3)*(T1 + T2 + T3)/cross(3)=3*91}}} Multiply both sides by 3.
4.{{{T1 + T2 + T3=273}}}
From equation 2, 
{{{(T1 + T2 + T3+T4+T5+T6)/6=94}}}
{{{cross(6)*(T1 + T2 + T3+T4+T5+T6)/cross(6)=6*94}}} Multiply both sides by 6.
5.{{{T1 + T2 + T3+T4+T5+T6=564}}}
From equation 4, you know that
{{{T1 + T2 + T3=273}}}
Substitute that into equation 5.
{{{T1 + T2 + T3+T4+T5+T6=564}}}
{{{(273+T4+T5+T6)=564}}}
{{{(cross(273)-cross(273)+T4+T5+T6)=564-273}}} Use the additive inverse of 273.
{{{T4+T5+T6=291}}}
If I divide both sides by 3, I'll get an equation that looks like equation (3). 
{{{(T4+T5+T6)/3=291/3=x}}}
{{{x=291/3}}}
{{{x=97}}}
Colin better start studying. He needs a 97 average on his last three tests to average 94.