Algebra Demystified 2nd Ed

Chapter 8 linear appliCaTionS 271

8. 100% 40% 60%

x^

ounces

+ 36 – x^

ounces

=^36

ounces

1.00x + 0.40(36 – x) = 0.60(36)

1000 40 36 06036

1001 44 04 0216

0

..().()

xx

xx

+−=

+− =

60 144216

144144

06072

72

06

12

x

x

x

x

+=

−−

=

=

=

Add 12 ounces of peanuts to 36 − x = 36 − 12 = 24 ounces of a 40% pea-

nut mixture to produce 36 ounces of a 60% peanut mixture.

Work Problems

Work problems are another staple of algebra courses. A work problem is nor-
mally stated as two workers (two people, machines, hoses, drains, etc.) working
together and working separately to complete a task. Usually one worker per-
forms faster than the other. Sometimes the problem states how fast each can
complete the task alone and we are asked to find how long it takes for them to
complete the task together. At other times, we are told how long one worker
takes to complete the task alone and how long it takes for both working together
to complete it; we are asked how long the second worker would take to com-
plete the task alone. The formula is quantity (work done—usually 1) = rate
times time: Q = rt. The method outlined below will help you solve most, if not
all, work problems. The chart shown is useful in solving these problems.

Worker Quantity Rate Time

1st Worker

2nd Worker

Together