The next example uses the idea of finding the average of a number of scores. In
general, to find the average of n numbers, add the numbers and divide by n.We use the
six problem-solving steps from Section 2.4,changing Step 3 to “Write an inequality.”
Finding an Average Test ScoreJohn Baker has grades of 86, 88, and 78 on his first three tests in geometry. If he
wants an average of at least 80 after his fourth test, what are the possible scores he
can make on that test?
Step 1 Readthe problem again.
Step 2 Assign a variable.Let x John’s score on his fourth test.
Step 3 Write an inequality.
is at
Average least 80.To find his average after four tests,
add the test scores and divide by 4.Step 4 Solve. Add in the numerator.
Multiply by 4.Subtract 252.
Combine like terms.Step 5 State the answer.He must score 68 or more on the fourth test to have an
average of at least80.
Step 6 Check.
(Also show that a score greater than 68 gives an average greater than 80.)
NOW TRY86 + 88 + 78 + 68
4
=
320
4
= 80
xÚ 68
252 + x- 252 Ú 320 - 252
252 + xÚ 320
4 a
252 +x
4
b Ú 41802
252 +x
4
Ú 80
86 + 88 + 78 +x
4
Ú 80
=
EXAMPLE 6
SECTION 2.8 Solving Linear Inequalities 157
CAUTION Do not confuse statements such as “5 is more than a number” with
the phrase “5 more than a number.” The first of these is expressed as while
the second is expressed as x+ 5 , or 5+x.
57 x,
NOW TRY
EXERCISE 6
Kristine has grades of 98 and
85 on her first two tests in
algebra. If she wants an
average of at least 90 after
her third test, what score
must she make on that test?
CAUTION In applied problems, remember that
at least translates as is greater than or equal to
and at most translates as is less than or equal to.
OBJECTIVE 6 Solve linear inequalities with three parts. Inequalities that
say that one number is betweentwo other numbers are three-part inequalities.For
example,
- 36567 says that 5 is between -3 and 7.
NOW TRY ANSWER
- 87 or more