SOLUTION: To make an A in a class, Colin must have at least an average of 94. On the first three tests he has an average of 91. What must he average on the last three tests to have an aver

Algebra ->  Average -> SOLUTION: To make an A in a class, Colin must have at least an average of 94. On the first three tests he has an average of 91. What must he average on the last three tests to have an aver      Log On


   

Question 101919: To make an A in a class, Colin must have at least an average of 94. On the first three tests he has an average of 91. What must he average on the last three tests to have an average of 94?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Write down what you know.
1.%28T1+%2B+T2+%2B+T3%29%2F3=91 Colin's average from first three tests.
2.%28T1%2BT2%2BT3%2BT4%2BT5%2BT6%29%2F6=94 Colin's average from first three and last three tests must equal at least 94.
3.%28T4+%2B+T5+%2B+T6%29%2F3=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,
%28T1+%2B+T2+%2B+T3%29%2F3=91
cross%283%29%2A%28T1+%2B+T2+%2B+T3%29%2Fcross%283%29=3%2A91 Multiply both sides by 3.
4.T1+%2B+T2+%2B+T3=273
From equation 2,
%28T1+%2B+T2+%2B+T3%2BT4%2BT5%2BT6%29%2F6=94
cross%286%29%2A%28T1+%2B+T2+%2B+T3%2BT4%2BT5%2BT6%29%2Fcross%286%29=6%2A94 Multiply both sides by 6.
5.T1+%2B+T2+%2B+T3%2BT4%2BT5%2BT6=564
From equation 4, you know that
T1+%2B+T2+%2B+T3=273
Substitute that into equation 5.
T1+%2B+T2+%2B+T3%2BT4%2BT5%2BT6=564
%28273%2BT4%2BT5%2BT6%29=564
%28cross%28273%29-cross%28273%29%2BT4%2BT5%2BT6%29=564-273 Use the additive inverse of 273.
T4%2BT5%2BT6=291
If I divide both sides by 3, I'll get an equation that looks like equation (3).
%28T4%2BT5%2BT6%29%2F3=291%2F3=x
x=291%2F3
x=97
Colin better start studying. He needs a 97 average on his last three tests to average 94.