Set 9(Page 15)
- b.According to the order of operations, we
perform exponentiation first, then multiplica-
tion, and then subtraction. The square of a
number x is x^2. Four times this quantity is 4x^2 ,
and finally, two less is 4x^2 – 2. - d.First, note that 25% ofVis equal to 0.25V,
which is equivalent to ^14 V. Since the original
volume of the tank is being increasedby this
quantity, we add it to the original volume V.
This results in the equivalent expressions V+
0.25Vand V+ ^14 V. Adding the coefficient ofV
in the first expression yields another equiva-
lent expression 1.25V.So, they are all correct
choices. - b.The amount of money paid for the total
number hours of tutoring is $40h. Adding the
one-time fee of $30 to this amount results in
x= $30 + $40h. - a.According to the order of operations, we
interpret parenthetical quantities first, then
multiply, and then subtract. The quantity the
sum of a number and 5is (x+ 5). Then, three
times this quantity is 3(x+ 5), and finally nine
less results in 3(x+ 5) – 9. - a.The total cost for a phone call lasting xmin-
utes is the cost for the first minute plus the cost
for the remaining x– 1 minutes. The first minute
costs $0.35 and the cost for the remaining x– 1
minutes is $0.15(x– 1). The sum of these results
in the total cost y = 0.15(x– 1) + 0.35. - b.According to the order of operations, we first
interpret parenthetical quantities and then mul-
tiply. The difference between a number and five
is represented by the expression (x – 5). Then,
half of this difference is ^12 (x – 5). - c.The sum of three numbers is represented by
(a+ b+ c). The reciprocals of these numbers
are ^1 a,^1 band ^1 c. The sum of the reciprocals is (^1 a
- ^1 b+ ^1 c), and so, the product of these two
sums is given by (a+ b+ c)(^1 a+ ^1 b+ ^1 c).
- c.The expression 3xis described by the phrase
“3 times a number.” So, the sum of 3x+ 15 is
described by the phrase “15 more than 3 times
a number.” Finally, since the word “is” is inter-
preted as “equals,” we conclude that the given
equation is described by choicec. - c.The cost for xdesks, each of which costs D
dollars, is xD. Similarly, the costs for the chairs
and file cabinets are yEand zF, respectively.
Thus, the total cost Tis equal to xD+ yE+ zF. - a.First, increasing dby 50% is described by
the expression d+ 0.50d,which is equal to
1.50d. Now, a decrease of this quantity by 50%
is described by the expression
1.50d– 0.50(1.50d) = 1.50d– 0.75d= 0.75dThis value is 75% of the original valued.Hence,
it is 25% smaller thand.- a.First, since there are w weeks in one month,
the number of weeks in m months must be
mw. Since we are told that there are m months
in one year, the quantity mwrepresents the
number of weeks in one year. Next, since there
are ddays in one week, and the number of
weeks in a year is mw, we conclude that there
are mwd days in one year. - d.The phrase “40% ofj” is expressed symboli-
cally as 0.40jand the phrase “50% ofk”is
expressed symbolically as 0.50k. Equating
these quantities yields the statement 0.40j=
0.50k. Dividing both sides by 0.40 then results
in the equivalent equality j= ^00 ..^54 ^00 k= 1.25k.
This says that the value ofj is 125% ofk.So,
we conclude that jis 25% larger than k.
ANSWERS & EXPLANATIONS–