Solve.
55)
Young’s rule, C =DA
A + 12 , can be used to approximate the dosage of a drug prescribed for
children. In this formula, A = child’s age in years, D = an adult dosage, and C = the proper child’s
dosage. When the adult dosage is 100 milligrams and the child’s dosage is 25 milligrams, what is
the child’s age?
55)
A)
4
B)
5
C)
6
D)
3
Solve the problem.
56)
56)
A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on
mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level
ground, find its rate in the mountains.
A)
40 mph
B)
80 mph
C)
20 mph
D)
50 mph
If y varies inversely as x, find the inverse variation equation for the situation.
57)
57)
y =30 when x =9
A)
y =270
x
B)
y =x
270
C)
y =10
3x
D)
y =1
270x
Simplify the rational expression.
58)
x2– 8x + 16
x2– 9x + 20
58)
A)
(x + 4)(x + 4)
(x – 5)(x – 4)
B)
x + 4
x + 5
C)
x – 4
x – 5
D)
(x – 4)(x – 4)
(x + 5)(x + 4)
Simplify the complex rational expression.
59)
59)
2
x+9
x2
4
x2–81
x
A)
1
2–9x
B)
2x2+9
4–81x
C)
2x +9
4–81x
D)
1
2x –9
Solve.
60)
60)
While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle
varies jointly as the mass of the passenger and the square of the speed of the car. If the a
passenger experiences a force of 112.5 newtons when the car is moving at a speed of 50
kilometers per hour and the passenger has a mass of 50 kilograms, find the force a passenger
experiences when the car is moving at 30 kilometers per hour and the passenger has a mass of
100 kilograms.
A)
90 newtons
B)
81 newtons
C)
99 newtons
D)
72 newtons
Find the least common denominator of the rational expressions.
61)
3
x2+ 3x
and 9
x2+ 9x + 18
61)
A)
x(x – 3)(x + 6)
B)
x(x + 3)2(x + 6)
C)
x(x – 3)2
D)
x(x + 3)(x + 6)
Solve the problem.
62)
62)
Park rangers catch, tag, and release 270 water buffalo back into a wildlife refuge. Two weeks later
they observe a sample of 180 buffalo, of which 9 are tagged. Assuming that the ratio of tagged
buffalo in the sample holds for all buffalo in the refuge, how many buffalo are there in the park?
A)
5400 buffalo
B)
4500 buffalo
C)
3600 buffalo
D)
7200 buffalo
Perform the indicated operation. Simplify the result, if possible.
63)
7y –7
(y –9)2÷y2– 1
y –9
63)
A)
7(y – 1)2(y + 1)
(y –9)3
B)
7
(y –9)(y – 1)
C)
7
(y –9)(y + 1)
D)
7
(y + 1)
Write an equation to describe the variation. Use k for the constant of proportionality.
64)
64)
m varies directly as x
A)
m=k
x
B)
m= kx
C)
x= km
D)
x=k
m
Simplify the rational expression. If the rational expression cannot be simplified, so state.
65)
2x + 3
10x2+ 21x + 9
65)
A)
2x + 5
5x + 21
B)
1
5x + 3
C)
2x
5x + 3
D)
cannot be simplified
Solve the rational equation.
66)
6
2x2+6x
= 1 –1
x +3
66)
A)
{6}
B)
{0}
C)
{–3, 1}
D)
{1}
Write an equation to describe the variation. Use k for the constant of proportionality.
67)
67)
s varies jointly as t and the square of u.
A)
s= k +t+u2
B)
s= ktu2
C)
s+t+u2= k
D)
stu2= k
Solve the rational equation.
68)
x2+2
x=18
x
68)
A)
B)
{–4, 0, 4}
C)
{–16, 16}
D)
{–4, 4}
Divide. Simplify if possible.
69)
(x +2) ÷x2–5x +6
3– x
69)
A)
–x –2
x +2
B)
–1
C)
–x +2
x –2
D)
–(x –2)(x +2)
Simplify the complex fraction.
70)
x
5
2
x + 3
70)
A)
x(x + 3)
10
B)
2x
5(x + 3)
C)
x + 3
10x
D)
10x(x + 3)
Perform the indicated operation. Simplify the result, if possible.
71)
x2+ x
x2+ 2x – 15
–x2+3
x2+ 2x – 15
71)
A)
x +5
B)
x –3
C)
1
x +5
D)
1
2(x +5)
21
Perform the indicated operation. Simplify if possible.
72)
5x +4
10 +7x –4
10
72)
A)
6x
5
B)
35x
5
C)
–6x
5
D)
12x
5
Solve the problem.
73)
73)
A boat moves 9 kilometers upstream in the same amount of time it moves 19 kilometers
downstream. If the rate of the current is 5 kilometers per hour, find the rate of the boat in still
water.
A)
5 kilometers per hour
B)
17 1
10 kilometers per hour
C)
41
2 kilometers per hour
D)
14 kilometers per hour
Simplify the rational expression. If the rational expression cannot be simplified, so state.
74)
6x – 18
15 – 5x
74)
A)
1
B)
–1
C)
6
5
D)
–6
5
Write an equation to describe the variation. Use k for the constant of proportionality.
75)
75)
r varies directly as s and inversely as the square of t.
A)
r=kt2
s
B)
rst2= k
C)
r+s–t2= k
D)
r=ks
t2
Perform the indicated operation(s). Simplify if possible.
76)
8y2
y – 1 –8y
y – 1
76)
A)
0
B)
8y(y + 1)
y – 1
C)
8y
D)
8y
y – 1
77)
2xy
x2– y2–y
x – y +8
2
77)
A)
4x + 5y
x + y
B)
(x – y)(4x + 5y)
x2– y2
C)
2xy – y + 4
x + y + 1
D)
4x + 5y
x2– y2
78)
x
x2– 25
+5
x + 5 –6
x
78)
A)
6x2– 25x + 150
x(x + 5)(x – 5)
B)
–25(x – 6)
x(x + 5)(x – 5)
C)
25(x + 6)
x(x + 5)(x – 5)
D)
25(x – 6)
(x + 5)(x – 5)
23
Write an equation to describe the variation. Use k for the constant of proportionality.
79)
79)
p varies directly as the square of q and inversely as the cube of r.
A)
pq2r3= k
B)
p+q2–r3= k
C)
p=kr3
q2
D)
p=kq2
r3
80)
80)
s varies jointly as t and the cube of u.
A)
s= ktu3
B)
s= k +t+u3
C)
s+t+u3= k
D)
stu3= k
Perform the indicated operation. Simplify the result, if possible.
81)
x2– 6x
x – 2 +8
x – 2
81)
A)
x2– 6x + 8
x – 2
B)
x – 4
C)
x + 4
D)
x – 2
82)
(x + y)2
x – y ÷x2+ xy
7x –7y
82)
A)
7x +7y
x2+ xy
B)
7x +7y
x
C)
7x –7y
x
D)
7x +7y
Perform the indicated operation(s). Simplify if possible.
83)
6
x2–7
x
83)
A)
6x + 7
x2
B)
6+ 7x
x2
C)
7x – 6
x
D)
6– 7x
x2
Use a proportion to solve the problem.
84)
84)
It is recommended that there be at least 16.8 square feet of ground space in a garden for every
newly planted shrub. A garden is 38.4 feet by 17.5 feet. Find the maximum number of shrubs the
garden can accommodate.
A)
2 shrubs
B)
192 shrubs
C)
13 shrubs
D)
40 shrubs
Perform the indicated operation(s). Simplify if possible.
85)
3
y2– 3y + 2
+7
y2– 1
85)
A)
42y – 11
(y – 1)(y + 1)(y – 2)
B)
11y – 10
(y – 1)(y + 1)(y – 2)
C)
10y – 11
(y – 1)(y + 1)(y – 2)
D)
10y – 11
(y – 1)(y – 2)
Solve the equation for the specified variable.
86)
1
a+1
b=1
c for c
86)
A)
c =a +
b
ab
B)
c = ab(a + b)
C)
c = a + b
D)
c =ab
a +
b
Perform the indicated operation(s). Simplify if possible.
87)
–1
7–4
9x
87)
A)
9x –28
63x
B)
–13
63 –9x
C)
–9x –28
63x
D)
–9x +28
63x
Simplify the rational expression.
88)
3x2+ 6x
5x2+ 12x + 4
88)
A)
3(x2+ 2x)
(5x + 2)(x + 2)
B)
cannot be simplified
C)
3
5x + 2
D)
3x
5x + 2
Simplify the complex fraction.
89)
y
5
6
y + 7
89)
A)
y(y + 7)
30
B)
y + 7
30y
C)
30y(y + 7)
D)
6y
5(y + 7)
Solve.
90)
90)
The amount of simple interest earned on an investment over a fixed amount of time is jointly
proportional to the principle invested and the interest rate. A principle investment of $1500.00
with an interest rate of 5% earned $300.00 in simple interest. Find the amount of simple interest
earned if the principle is $4100.00 and the interest rate is 8%.
A)
$1312.00
B)
$131,200.00
C)
$480.00
D)
$820.00
Perform the indicated operation(s). Simplify if possible.
91)
1
4x – 8 –6
5x + 5 +4
3x + 6
91)
A)
167x2– 35x + 158
12x + 19
B)
23x2– 35x + 158
60(x – 2)(x + 1)(x + 2)
C)
167x2– 35x + 158
60(x – 2)(x + 1)(x + 2)
D)
23x2– 35x + 13
12x + 19
Find the least common denominator of the rational expressions.
92)
2
25x3 and 5
15x7
92)
A)
75x10
B)
75x3
C)
75x7
D)
25x7
Solve.
93)
93)
If the resistance in an electrical circuit is held constant, the amount of current flowing through the
circuit is directly proportional to the amount of voltage applied to the circuit. When 4 volts are
applied to a circuit, 100 milliamperes of current flow through the circuit. Find the new current if
the voltage is increased to 9 volts.
A)
250 milliamperes
B)
216 milliamperes
C)
225 milliamperes
D)
36 milliamperes
Add or subtract as indicated. Simplify the result, if possible.
94)
x
x2–16
–4
16 –x2
94)
A)
–1
x –4
B)
1
x +4
C)
1
x –4
D)
–1
x +4
Write an equation to describe the variation. Use k for the constant of proportionality.
95)
95)
z varies inversely as w
A)
w=z
k
B)
w= kz
C)
z=w
k
D)
z=k
w
Solve the problem.
96)
96)
A baker can decorate the day‘s cookie supply four times as fast as his new assistant. If they
decorate all the cookies working together in 28 minutes, how long would it take for each of them
to decorate the cookies working individually?
A)
baker: 140 minutes
assistant: 560 minutes
B)
baker: 81
4 minutes
assistant: 33 minutes
C)
baker: 35 minutes
assistant: 140 minutes
D)
baker: 140 minutes
assistant: 35 minutes
Simplify the rational expression. If the rational expression cannot be simplified, so state.
97)
7x3
14x8
97)
A)
1
2x5
B)
x5
2
C)
1
2
D)
1
2x11
Simplify the complex rational expression.
98)
1
6+1
4
1
7+1
2
98)
A)
12
7
B)
54
35
C)
35
54
D)
7
12
Add or subtract as indicated. Simplify the result, if possible.
99)
5
x –7+4
7– x
99)
A)
9
x –7
B)
1
x –7
C)
–1
x –7
D)
–1
7– x
Solve the rational equation.
100)
x2–5
3x = – 1
3x
100)
A)
{2}
B)
C)
{–2, 2}
D)
{–2, 0, 2}
Solve the problem.
101)
101)
Julie and Eric row their boat (at a constant speed) 21 miles downstream for 3 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of
the current.
A)
3 mph
B)
5 mph
C)
2 mph
D)
1.5 mph
If y varies inversely as x, find the inverse variation equation for the situation.
102)
y =1
8 when x =56
102)
A)
y =7
x
B)
y =1
448 x
C)
y =1
7x
D)
y =x
7
Solve the rational equation.
103)
7x
x +4–28
x –4=7x2+112
x2–16
103)
A)
{4, –4}
B)
{–4}
C)
{4}
D)
Simplify the rational expression. If the rational expression cannot be simplified, so state.
104)
4x –8
x2–5x +6
104)
A)
cannot be simplified
B)
4(x –8)
x +3
C)
4
x +3
D)
4
x –3