Five students wrote a mathematics test. The average mark was 68. If the marks for four of the students were 75, 62, 84 and 53, the mark of the fifth student was

66

Step-by-step explanation:

Use the formula for the mean of a set of numbers:

                  sum of the numbers

average =

                     count of numbers

Here we know that the average mark was 68, so we can write:

                           75 + 62 + 84 + 53 + x

average = 68 =

                                           5

or                            274 + x

                  68 =

                                    5

Solving for x, we multiply both sides by 5:     340 = 274 + x.

Subtracting 274 from both sides effectively isolates x:

 340 = 274 + x

- 274    -274

  66      =    x

The fifth student's mark was 66.