Deck 19: Ratio, Proportion, and Variation

Question 1

Find $x$ where $x:(8+x)=1: 5$ .

Answer 1

2

Question 2

Find $x$ where $9: x=13.5: 2$ .

Answer 2

$4 / 3$

Question 3

Find the missing quantity: $\frac{5}{3 a}: \frac{?}{5 a}$

Answer 3

$25 / 3$

Question 4

Find the value of $x$ where $5: 7=x: 42$ .

Question 5

Find the value of $x: x: 10=(x+8): 18$

Question 6

Find the missing quantity: $\frac{?}{9 x}: \frac{14}{63 x}$

Question 7

Find the missing quantity: $\frac{4 x}{x-1}: \frac{4}{\text { ? }}$

Question 8

Find the missing quantity: $\frac{12 x}{?}: \frac{1.8 x}{0.3}$

Question 9

Find the missing quantity: $\frac{3 x}{?}: \frac{2.4 x}{0.5}$

Question 10

Find the mean proportional between 2 and 72 .

Question 11

Find the mean proportional between 4 and 100 .

Question 12

Find the mean proportional between 16 and 64 .

Question 13

Find the mean proportional between 10 and 40 .

Question 14

Find the mean proportional between 2 and 32 .

Question 15

Find the mean proportional between 21 and 84 .

Question 16

Find two numbers that are to each other as $4: 7$ and whose sum is 66 .

Question 17

Find two numbers that are to each other as $12: 19$ and whose difference is 49 .

Question 18

The difference of two numbers is 54 and the smaller is to the larger as one is to three. What are the numbers?

Question 19

Divide $\$ 240$ into two parts where the smaller is to the greater as 3 is to 5 .

Question 20

If $(m+n):(m-n)=11: 3$ , determine the ratio $m: n$ .

Question 21

If $(m-n):(m+n)=2: 5$ , determine the ratio $m: n$ .

Question 22

Determine the values for $x$ and $y$ given that $x: 5: 7=10: y: 35$ .

Question 23

Determine the values for $a$ and $b$ given that $2: a: 3=8: 16: b$ .

Question 24

Determine the values for $a$ and $b$ given that $6: 7: a=b: 21: 24$ .

Question 25

Determine the values of $x, y, z$ , and $u$ given that $x+y+z+u=90$ and $x: y: z: u=3: 4: 5: 6$ .

Question 26

Determine the values of $x, y$ , and $z$ given that $x: y: z=3: 5: 7$ and $5 x+2 y+3 z=598$ .

Question 27

Determine the values of $a, b$ , and $c$ if $a: b: c=1: 4: 9$ and $2 a+3 b-c=4$ .

Question 28

If $y$ varies directly as $x$ and $y$ is 17 when $x$ is 59.5 , find $y$ when $x$ is 8.75 .

Question 29

If $y$ varies directly as $x$ and $y$ is 42 when $x$ is 36 , find $y$ when $x$ is 54 .

Question 30

If $y$ varies directly as $x$ and $x$ is 15 when $y$ is 27 , find $x$ when $y$ is 432 .

Question 31

If $x$ is directly proportional to $y$ and $x$ is 3.24 when $y$ is 923 , find $x$ when $y$ is 323 .

Question 32

If $m$ is directly proportional to $n$ and $m$ is 4 when $n$ is 32 , find $m$ when $n$ is 48 .

Question 33

If $x$ is directly proportional to $y$ and $x$ is 1.28 when $y$ is 32.0 , find $x$ when $y$ is 13.1 .

Question 34

Assume $y$ is directly proportional to $x$ and $y$ is 22.3 when $x$ is 22.9 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=3210$ .
(d) Find $x$ when $y=4321$ .

Question 35

If $y$ varies directly as $x$ and $y$ is 45 when $x$ is 3 , find $y$ when $x$ is 6 .

Question 36

If $y$ varies directly as $x$ and $y$ is 54 when $x$ is 3 , find $y$ when $x$ is 2.5 .

Question 37

Assume $y$ is directly proportional to $x$ and $y$ is 33.11 when $x$ is 15.05 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=562.5$ .
(d) Find $x$ when $y=152.46$ .

Question 38

Assume $y$ is directly proportional to $x$ and $y$ is 75.4 when $x$ is 1.45 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=16.3$ .
(d) Find $x$ when $y=234$ .

Question 39

A car uses $6.9 \mathrm{~L}$ of fuel to travel go $10 \overline{0} \mathrm{~km}$ . How far can the car go on $32 \mathrm{~L}$ of fuel?

Question 40

A car uses $7.1 \mathrm{~L}$ of fuel to travel go $10 \overline{0} \mathrm{~km}$ . How much fuel will it use to travel $364 \mathrm{~km}$ ?

Question 41

The weight of a piece of sheet metal with given thickness is proportional to its area. If a sheet of copper with dimensions $2.5 \mathrm{~m} \times 3.4 \mathrm{~m}$ weighs $45 \mathrm{~kg}$ , what is the weight of a sheet of copper with the same thickness, length $5 \mathrm{~m}$ , and width $1.7 \mathrm{~m}$ ?

Question 42

If a certain machine can make 172 parts in 38 minutes, how many parts can it make in 8 hours?

Question 43

The actual distance between the two cities is $128 \mathrm{~km}$ , but they are $2.50 \mathrm{~cm}$ apart on the map. Find the actual distance between two points that are $12.0 \mathrm{~cm}$ apart on the same map.

Question 44

The scale on a map shows that $1.2 \mathrm{~cm}$ represents $155 \mathrm{~km}$ . If two cities are $365 \mathrm{~km}$ apart, how far apart will they appear on the map?

Question 45

If $y$ varies directly as the square of $x$ and $y$ is 616 when $x$ is 34.0 , find $y$ when $x$ is 99.0 .

Question 46

If $y$ varies directly as the cube of $x$ and $y$ is 15.6 when $x$ is 1.07 , find $y$ when $x$ is 6.88 .

Question 47

If $y$ varies directly as the square of $x$ and $y$ is 45 when $x$ is 3 , find $y$ when $x$ is 6 .

Question 48

If $y$ varies directly as the cube of $x$ and $y$ is 54 when $x$ is 3 , find $y$ when $x$ is 2.5 .

Question 49

If $y$ is directly proportional to the square of $x$ and has a value of 22 when $x$ is 3 , find $y$ when $x$ is 5 .

Question 50

If $y$ is directly proportional to the cube of $x$ and has a value of 222 when $x$ is 9.33 , find $y$ when $x$ is 18.6 .

Question 51

If $y$ varies directly as the square root of $x$ and $y$ is 33.1 when $x$ is 274 , find $y$ when $x$ is 145 .

Question 52

Assume $y$ is directly proportional to the $3 / 2$ power of $x$ and has a value of 3.22 when $x$ is 30.9 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=40.3$ .
(d) Find $x$ when $y=2.79$ .

Question 53

Assume $y$ is directly proportional to the 4 th power of $x$ and has a value of 155.58 when $x$ is 4.2 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=0.4$ .
(d) Find $x$ when $y=75.03$ .

Question 54

Assume $y$ is directly proportional to the 5th power of $x$ and has a value of 20.42 when $x$ is 2.10 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=1.48$ .
(d) Find $x$ when $y=5.22$ .

Question 55

If a body falls $225 \mathrm{~m}$ in the first five seconds after it is dropped, how far does it fall in the next five seconds?

Question 56

If a body falls $270 \mathrm{ft}$ in $4 \mathrm{~s}$ , how far will it fall in $11 \mathrm{~s}$ ?

Question 57

A certain window admits 10 watts of sunlight. By how much should every dimension of the window be increased to make the window admit 22 watts of sunlight?

Question 58

A certain photograph will be correctly exposed at a shutter speed of $0.01 \mathrm{~s}$ at a lens opening of $\mathrm{f2.8}$ . What lens opening is needed for a shutter speed of $0.04 \mathrm{~s}$ ?

Question 59

If it costs $\$ 156$ to put a fence around a square field, how much will it cost to put a fence around another square field having three times the area?

Question 60

The time $t$ for the swing of a simple pendulum varies directly as the square root of the length $L$ . If the time of the swing is $1.5 \mathrm{~s}$ when the length is $8 \mathrm{~cm}$ , find the time of the swing when the length of the pendulum is $1.2 \mathrm{~cm}$ .

Question 61

Two polygons are similar. One has area $56.5 \mathrm{~cm}^{2}$ and the other one has area $175 \mathrm{~cm}^{2}$ . A side length in the smaller polygon is $4.30 \mathrm{~cm}$ . What is the length of the corresponding side in the larger polygon?

Question 62

Two prisms are similar. The volume of one is $157.5 \mathrm{~m}^{3}$ while the other has a volume of $53.2 \mathrm{~cm}^{3}$ . If the surface area of the smaller prism is $89.4 \mathrm{~cm}^{2}$ , what is the surface area of the larger prism?

Question 63

If $y$ is inversely proportional to $x$ and has a value of 6.8 when $x$ is 3.2 , find $y$ when $x$ is 20 .

Question 64

If $y$ is inversely proportional to the square of $x$ and has a value of 901 when $x$ is 211 , find $y$ when $x$ is 103 .

Question 65

If $y$ varies inversely as $x$ and $y$ is 72 when $x$ is 32 , find $y$ when $x$ is 96 .

Question 66

If $y$ is inversely proportional to the cube of $x$ and $y$ is 0.50 when $x$ is 2.0 , find $y$ when $x$ is 5.0 .

Question 67

If $y$ varies inversely as $x$ and $y$ is 94 when $x$ is 582 , find $y$ when $x$ is 116 .

Question 68

If $y$ is inversely proportional to the square of $x$ and $y$ is 153 when $x$ is 28.0 , find $y$ when $x$ is 100 .

Question 69

Assume $y$ is inversely proportional to the square of $x$ and has a value of 2200 when $x$ is 30.9 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=132$ .
(d) Find $x$ when $y=36.2$ .

Question 70

Assume $y$ is inversely proportional to the cube of $x$ and has a value of 3.25 when $x$ is 5.50 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=10.2$ .
(d) Find $x$ when $y=6.125$ .

Question 71

Assume $y$ is inversely proportional to the square root of $x$ and has a value of 15.4 when $x$ is 1.25 .
(a) Find the constant of proportionality.
(b) Write the equation $y=\mathrm{f}(x)$ .
(c) Find $y$ when $x=7.25$ .
(d) Find $x$ when $y=9.50$ .

Question 72

If the gravitational force between two objects is $1.05 \times 10^{-9} \mathrm{~N}$ when the objects are $9.39 \mathrm{~cm}$ apart, how far apart should the objects be placed to make the force between them equal $4.32 \times 10^{-9} \mathrm{~N}$ ?

Question 73

A certain light source produces an illumination of 235 lumens on a surface. Find the illumination of the surface when the source is moved 3.20 times closer.

Question 74

When a gas expands at a constant temperature its pressure varies inversely as its volume. If the pressure of a certain gas is $40 \mathrm{~kg} / \mathrm{m}^{2}$ when its volume is $0.8 \mathrm{~m}^{3}$ , determine the pressure when the volume of the gas is $0.1 \mathrm{~m}^{3}$ ?

Question 75

When a certain quantity of gas is compressed to a volume of $0.82 \mathrm{~m}^{3}$ , it has a pressure of $76 \mathrm{~Pa}$ . Find the pressure of the gas when it is compressed to $0.55 \mathrm{~m}^{3}$ . (Assume a constant temperature.)

Question 76

The frequency of a sound wave travelling through a medium varies inversely as the wavelength. If the frequency is $433 \mathrm{~Hz}$ when the wavelength is $0.700 \mathrm{~m}$ , what is the frequency when the wavelength is $1.20 \mathrm{~m}$ ?

Question 77

The frequency of a sound wave travelling through a medium varies inversely as the wavelength. If the frequency is $243 \mathrm{~Hz}$ when the wavelength is $0.500 \mathrm{~m}$ , what is the wavelength when the frequency is $320 \mathrm{~Hz}$ ?

Question 78

The force of gravity between two objects is inversely proportional to the square of the distance between them. If the force of gravity between two objects is $3.27 \times 10^{-7} \mathrm{~N}$ when the distance is $1.00 \mathrm{~m}$ , what is the force when the distance is $0.200 \mathrm{~m}$ ?

Question 79

If a certain machine can produce 36000 units in 2.7 hours, how many hours will it take three of the same type machines to produce the same number of units?

Question 80

If 25000 parts are produced in 5.25 hours by five machines, find the number of parts produced by one machine in the same time?