Question

If Ernest is suppose to have 75 in sic courses to obtain an A but he has 73 in 5 courses, then what should be his score in the 6 course to still obtain an A?

Answer 1

Just write the expression that describes his 75% in six courses required to obtain A:

$$75=\frac{n_1+n_2+...+n_6}{6},$$

where n₁, n₂, ..., n₆ - his individual mark for each course.

75% is the average percentage he wants to obtain for 6 courses whatever the individual mark is. 73% he obtained for 5 courses, and we don't care what each individual mark during 5 courses was:

$$73=\frac{n_1+n_2+...+n_5}{5}.$$

We need to find n₆ to tell him what mark he must obtain. From the first expression it is

$$n_6=75\cdot6-(n_1+n_2+...+n_5),$$

from the second equation we have

$$n_1+n_2+...+n_5=73\cdot5.$$

Substitute this to the third equation:

$$n_6=75\cdot6-73\cdot5=85.$$

He needs to obtain 85% to get A.