To solve application problems, we let a variable stand for an unknown quantity.642 Chapter 8 An Introduction to Algebra
EXAMPLE (^3) Write each phrase as an algebraic expression:
a.one-half of the profit
b.5 less than the capacity
c.the product of the weight and 2,000, increased by 300
StrategyWe will begin by identifying any key phrases.
WHYKey phrases can be translated to mathematical symbols.
Solution
a.Key phrase:One-half of Translation:multiplication by
The algebraic expression is:.
b.Key phrase:less than Translation:subtraction
Sometimes thinking in terms of specific numbers makes translating easier.
Suppose the capacity was 100. Then 5 less than100 would be. If the
capacity is , then we need to make c5 less. The algebraic expression is:.
Caution! is the translation of the statement 5 is less than the
capacity and not 5less than the capacity.
c.Key phrase:product of Translation:multiplication
Key phrase:increased by Translation:addition
In the given wording, the comma after 2,000 means is first multiplied
by 2,000; then 300 is added to that product. The algebraic expression is:
2,000w 300.
w
c c
5 c
c c 5
100 5
12 P
(^12)
w
c
P
Self Check 3
Write each phrase as an
algebraic expression:
a.80 less than the total
b. of the time
c.the difference of twice
and 15, squared
Now TryProblems 31, 37, and 41a(^23) T
t
Self Check 4
COMMUTING TO WORK It takes
Val mminutes to get to work
if she drives her car. If she takes
the bus, her travel time exceeds
this by 15 minutes. How long
does it take her to get to
work by bus?
Now TryProblem 67
Self Check 5
SCHOLARSHIPSPart of a $900
donation to a college went to the
scholarship fund, the rest to the
building fund. Choose a variable
to represent the amount donated
to one of the funds. Then write an
expression that represents the
amount donated to the other fund.
Now TryProblem 12
EXAMPLE (^4) Swimming A
pool is to be sectioned into 8 equally
wide swimming lanes. Write an algebraic
expression that represents the width of
each lane.
StrategyWe will begin by letting the width of the swimming pool in feet.
Then we will identify any key phrases.
WHYThe width of the pool is unknown.
SolutionThe key phrase,sectioned into 8 equally wide lanes,indicates division.
Therefore, the width of each lane is feet. x 8
x
x
EXAMPLE (^5) Painting A 10-inch-long paintbrush has two parts: a
handle and bristles. Choose a variable to represent the length of one of the parts.
Then write an expression to represent the length of the other part.
StrategyThere are two approaches. We can let the length of the handle or we
can let the length of the bristles.
WHYBoth the length of the handle and the length of the bristles are unknown.
b
h