Chapter 8 linear appliCaTionS 251
- Monica’s earnings are being compared to John’s, and John’s to Alicia’s.
The easiest thing to do is to let x represent Alicia’s hourly wage, so John’s
hourly wage is x + 2. Monica earns three times as much as John, so her
hourly wage is 3(x + 2).
xx x
xx x
x
x
x
++++=
++++=
+=
−−
=
()() 23 243
23 643
5843
88
535
==
=
35
5
x 7
Alicia earns $7 per hour; John, x + 2 = 7 + 2 = $9; and Monica 3(x + 2) =
3(7 + 2) = $27.
Grade Problems
Grade computation problems are probably the most useful problem types to
students. In these problems, the formula for the course grade and all but one
grade are given. We are asked to compute the unknown grade in order to
ensure a particular course average.
EXAMPLE
A student has grades of 72, 74, 82, and 90. What does the next grade have
to be to obtain an average of 80?
We take the average of five numbers: 72, 74, 82, 90 and the next grade.
Call this next grade x. We want this average to be 80.
72 74 82 90
5
80
318
5
80
++++=
+ =
x
x
5318
5
+ 580
x = ()
318 400
318 318
+=
−−
x
x= 82
The student needs an 82 to raise his/her average to 80.
EXAMPLE
A student has grades of 72, 74, 82, and 90. What does the next grade have
