Chapter ISG, Problem 5.3.4P

To determine

To write and solve an inequality to determine score needed by M in her next exam so that her average is at least 82.

Answer to Problem 5.3.4P

The inequality can be written as $(76+80+78+x)÷4\ge 82$

She needs at least $x\ge 94$ so that her average is at least 82

Explanation of Solution

Given information:

M got scores of 76, 80 and 78 in her last three history exams

Calculation:

Let M’s score in her next exam be $x$

Average of 4 exams is equal to $(76+80+78+x)÷4$

According to question:-

  $(76+80+78+x)÷4\ge 82$

Solving it further

  $(234+x)÷4\ge 82$

On multiplying both sides by 4

  $(234+x)÷4\times 4\ge 82\times 4$

Solving it further

  $(234+x)\times 1\ge 328$

The inequality can be expressed as

  $234+x\ge 328$

On subtracting 234 from both sides

  $234+x-234\ge 328-234$

The final answer is

  $x\ge 94$

Therefore M requires to score at least 94 marks in her next exam so that her average is at least 82