Deck 7: Ratio and Proportion

Question 1

Find the flow rate for the given IV (intravenous), assume a drop factor of 15 drops/mL. Round your answer to the nearest whole number. 1,100 mL in 8 h

A) 34 drops/min
B) 33 drops/min
C) 138 drops/min
D) 37 drops/min
E) 39 drops/min

Answer 1

34 drops/min

Question 2

A welder grabs a handful of 6011 welding rods and another handful of Super Strength 100 welding rods. When the welder sees how many of each she has, she has 26 of the 6011 welding rods and 90 of the Super Strength 100 welding rods. What is the ratio of the 6011 welding rods to the Super Strength 100 welding rods?

A) $\frac { 11 } { 47 }$
B) $\frac { 3 } { 25 }$
C) $\frac { 7 } { 39 }$
D) $\frac { 9 } { 41 }$
E) $\frac { 13 } { 45 }$

Answer 2

$\frac { 13 } { 45 }$

Question 3

Express the ratio in lowest terms. $22 \text { to } 18$

A) $\frac { 22 } { 9 }$
B) $\frac { 11 } { 9 }$
C) $\frac { 13 } { 7 }$
D) $\frac { 17 } { 15 }$
E) $\frac { 7 } { 13 }$

Answer 3

$\frac { 11 } { 9 }$

Question 4

Express the ratio in lowest terms. $7 \frac { 8 } { 9 } : 9$

A) $\frac { 65 } { 78 }$
B) $\frac { 65 } { 75 }$
C) $\frac { 69 } { 79 }$
D) $\frac { 75 } { 85 }$
E) $\frac { 71 } { 81 }$

Question 5

Find the length of time an IV (intravenous) should be administered. (Assume a drop factor of 10 drops/mL.) Give your answer in hours. 780 mL at a rate of 30 drops/min

A) $\frac { 1 } { 3 } \text { hours }$
B) $3 \frac { 1 } { 3 } \text { hours }$
C) $4 \frac { 1 } { 3 } \text { hours }$
D) $7 \frac { 1 } { 3 } \text { hours }$
E) $2 \frac { 1 } { 3 } \text { hours }$

Question 6

Express the ratio in lowest terms. $9 \frac { 1 } { 2 } : 8 \frac { 1 } { 2 }$

A) $\frac { 19 } { 17 }$
B) $\frac { 25 } { 11 }$
C) $\frac { 21 } { 19 }$
D) 9
$$8$$
E) $\frac { 23 } { 13 }$

Question 7

Two small window air conditioner units are purchased and put into opposite sides of a house. One air conditioner is 2,000 Btu and the other is 6,500 Btu. What is the ratio of the 2,000 Btu to the 6,500 Btu air conditioner?

A) $\frac { 4 } { 13 }$
B) $\frac { 1 } { 50 }$
C) $\frac { 2 } { 15 }$
D) $\frac { 10 } { 19 }$
E) $\frac { 8 } { 17 }$

Question 8

Express the ratio in lowest terms. $5 : 40$

A) $\frac { 1 } { 8 }$
B) $\frac { 1 } { 13 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 11 }$
E) $\frac { 1 } { 7 }$

Question 9

The total hours for a Private pilot, single engine land rating for a single engine airplane is 90 h of flight time. The total hours of flight time for a Commercial rating is 340 h. What is the ratio of the hours for a Private rating to the hours for a Commercial rating?

A) $\frac { 9 } { 34 }$
B) $\frac { 15 } { 40 }$
C) $\frac { 13 } { 30 }$
D) $\frac { 7 } { 32 }$
E) $\frac { 34 } { 9 }$

Question 10

A 400 bu wagon holds 9.2 tons of grain. Express the weight of grain in pounds per bushel.

A) 45 lb/bu
B) 43 lb/bu
C) 92 lb/bu
D) 51 lb/bu
E) 46 lb/bu

Question 11

Express the ratio in lowest terms. $2 \mathrm {~cm} \text { to } 10 \mathrm {~mm}$

A) $\frac { 2 } { 1 }$
B) $\frac { 5 } { 1 }$
C) $\frac { 10 } { 1 }$
D) $\frac { 4 } { 1 }$
E) $\frac { 1 } { 1 }$

Question 12

Express the ratio in lowest terms. $6 \frac { 6 } { 9 } : 30$

A) $\frac { 8 } { 3 }$
B) $\frac { 6 } { 13 }$
C) $\frac { 4 } { 11 }$
D) $\frac { 60 } { 9 }$
E) $\frac { 2 } { 9 }$

Question 13

Find the flow rate for the given IV (intravenous), assume a drop factor of 15 drops/mL. Round your answer to the nearest whole number. 2 L in 7 h

A) 71 drops/min
B) 72 drops/min
C) 76 drops/min
D) 68 drops/min
E) 7 drops/min

Question 14

The ratio of the voltage drops across two resistors wired in series equals the ratio of their resistances. Find the ratio of a 690- ? resistor to a 300- ? resistor.

A) $\frac { 25 } { 3 }$
B) $\frac { 27300 } { 14300 }$
C) $\frac { 23 } { 10 }$
D) $\frac { 21300 } { 8300 }$
E) $\frac { 17300 } { 16300 }$

Question 15

Find the length of time an IV (intravenous) should be administered. (Assume a drop factor of 10 drops/mL.) Give your answer in hours. 2.1 L at a rate of 60 drops/min

A) $3 \frac { 5 } { 6 } \text { hours }$
B) $5 \frac { 5 } { 6 } \text { hours }$
C) $4 \frac { 5 } { 6 } \text { hours }$
D) $8 \frac { 5 } { 6 } \text { hours }$
E) $50 \frac { 5 } { 6 } \text { hours }$

Question 16

You need 25 ft ³ of cement to make 70 ft ³ of concrete. Find the ratio of volume of concrete to volume of cement.

A) $\frac { 5 } { 14 }$
B) $\frac { 10 } { 9 }$
C) $\frac { 20 } { 11 }$
D) $\frac { 16 } { 7 }$
E) $\frac { 14 } { 5 }$

Question 17

Express the rate in lowest terms. $\frac { 800 \mathrm { mi } } { 8 \mathrm { gal } }$

A) $85 \frac { \mathrm { mi } } { \mathrm { gal } }$
B) $90 \frac { \mathrm { mi } } { \mathrm { gal } }$
C) $105 \frac { \mathrm { mi } } { \mathrm { gal } }$
D) $200 \frac { \mathrm { mi } } { \mathrm { gal } }$
E) $100 \frac { \mathrm { mi } } { \mathrm { gal } }$

Question 18

Express the ratio in lowest terms. $8 \text { to } 5 \frac { 3 } { 4 }$

A) $\frac { 26 } { 29 }$
B) $\frac { 36 } { 27 }$
C) $\frac { 8 } { 23 }$
D) $\frac { 32 } { 23 }$
E) $\frac { 34 } { 25 }$

Question 19

Suppose 165 gal of oil flow through a feeder pipe in 5 min. Find the flow rate in gallons per minute.

A) 38 gal/min
B) 66 gal/min
C) 36 gal/min
D) 34 gal/min
E) 33 gal/min

Question 20

Express the rate in lowest terms. $\frac { \$ 64,600 } { 1,700 \mathrm { ft } ^ { 2 } }$

A) $38/ft ²
B) $380/ft ²
C) $37/ft ²
D) $41/ft ²
E) $43/ft ²

Question 21

A salesperson is paid a commission of $90 for selling $360 worth of goods. What is the commission on $880 of sales at the same rate of commission?

A) $225
B) $440
C) $220
D) $230
E) $235

Question 22

Solve the proportion. Round the result to three significant digits when necessary. $\frac { x } { 32 } = \frac { 63 } { 81 }$

A) x = 26.0
B) x = 0.040
C) x = 24.9
D) x = 27.2
E) x = 21.3

Question 23

Express the ratio in lowest terms. $39 \text { to } 33$

Question 24

Express the rate in lowest terms. __________ mi/gal

Question 25

Solve the proportion. Round the result to three significant digits when necessary. $\frac { 18 } { 20 } = \frac { 126 } { 2 x }$

A) x = 69
B) x = 75
C) x = 70
D) x = 140
E) x = 67

Question 26

Express the ratio in lowest terms. $4 \text { to } 3 \frac { 1 } { 2 }$

Question 27

Find the length of time an IV (intravenous) should be administered. (Assume a drop factor of 10 drops/mL.) Give your answer in hours and express part of an hour as a fraction.
1.29 L at a rate of 30 drops/min

Question 28

Solve the proportion. Round the result to three significant digits when necessary. $\frac { 5 } { 9 } = \frac { 10 } { y }$

A) y = 17.7
B) y = 18.1
C) y = 0.1
D) y = 18
E) y = 18.5

Question 29

Solve the proportion. Round the result to three significant digits when necessary. $\frac { 0.18 } { 2 x } = \frac { 0.545 } { 278 }$

A) x = 28.3
B) x = 29.5
C) x = 30.6
D) x = 27.0
E) x = 91.8

Question 30

Find the flow rate for the given IV (intravenous), assuming a drop factor of 15 drops/mL. Round your answer to the nearest whole number.
1,100 mL in 4 h
__________ drops/minute

Question 31

Solve the proportion. Round the result to three significant digits when necessary. $\frac { - 9 } { x } = \frac { 2 } { 9 }$

A) x = 40
B) x = -40.5
C) x = -42
D) x = 40.5
E) x = -39.5

Question 32

Solve the proportion. Round the result to three significant digits when necessary. $\frac { 94.8 } { 6.78 } = \frac { x } { 19.3 }$

A) x = 273
B) x = 271
C) x = 33.3
D) x = 268
E) x = 270

Question 33

Find the length of time an IV (intravenous) should be administered. (Assume a drop factor of 10 drops/mL.) Give your answer in hours and express part of an hour as a fraction.
560 mL at a rate of 40 drops/min

Question 34

Express the rate in lowest terms. __________ $/

Question 35

Express the ratio in lowest terms. $2 : 14$

Question 36

The ratio of the voltage drops across two resistors wired in series equals the ratio of their resistances. Find the ratio of a 1,750- Ω resistor to a 700- Ω resistor.

Question 37

Solve the proportion. Round the result to three significant digits when necessary. $\frac { x } { 10 } = \frac { 3 } { 5 }$

A) x = 7
B) x = 1
C) x = 6
D) x = 3
E) x = 0.167

Question 38

Express the ratio in lowest terms. $12 \mathrm {~cm} \text { to } 15 \mathrm {~mm}$

Question 39

Solve the proportion. Round the result to three significant digits when necessary. $\frac { 30 } { 35 } = \frac { y } { 42 }$

A) y = 36
B) y = 37
C) y = 0.028
D) y = 31
E) y = 39

Question 40

Find the flow rate for the given IV (intravenous), assume a drop factor of 15 drops/mL. Round your answer to the nearest whole number.
2 L in 7 h
__________ drops/minute

Question 41

If welding rods cost $59 per 50 lb, how much would it cost for 90 lb?

A) $111.20
B) $106.20
C) $104.20
D) $113.70
E) $102.70

Question 42

Find the amount of pure ingredient needed to prepare the solution as indicated.
750 mL of 1 : 50 sodium bicarbonate solution from pure sodium bicarbonate
__________ mL

Question 43

A farmer uses 180 lb of a chemical on a 40-acre field. How many pounds will he need for a 220-acre field? Assume the same rate of application.
__________ lb

Question 44

Solve the proportion. y = __________

Question 45

Solve the proportion. Round the result to three significant digits. __________

Question 46

8 in. x 20 in. metal duct costs $13.40 for four feet. If 14.5 ft are needed for an order, what is the cost? Round your answer to the nearest cent.

A) $48.58
B) $51.99
C) $53.70
D) $49.71
E) $48.08

Question 47

A car uses 18 gal of gas to go 580 mi. How many gallons are required to go 810 mi? Round your answer to nearest tenth.

A) 30.4 gallons
B) 26.2 gallons
C) 25.1 gallons
D) 21.9 gallons
E) 12.9 gallons

Question 48

A car is listed to sell at $23,600. The salesperson offers to sell it to you for $18,300. What percent of the list price is the reduction? Round your answer to the nearest tenth of a percent if necessary.
__________ %

Question 49

Solve the proportion. Round the result to three significant digits. __________

Question 50

Find the amount of pure ingredient needed to prepare the solution as indicated. 230 mL of 8% Lysol solution from pure Lysol

A) 1,840.0 mL
B) 18.4 mL
C) 21.7 mL
D) 20.6 mL
E) 19.5 mL

Question 51

The ratio of secondary turns to primary turns in a transformer is 37 to 2. How many secondary turns are there if the primary coil has 38 turns?

A) 700 turns
B) 703 turns
C) 710 turns
D) 698 turns
E) 688 turns

Question 52

A farmer uses 170 lb of a chemical on a 40 acre field. How many pounds will he need for a 240-acre field? Assume the same rate of application.

A) 1,030 lb
B) 1,015 lb
C) 1,020 lb
D) 970 lb
E) 1,035 lb

Question 53

Solve the proportion. $\frac { 5 } { 9 } = \frac { 6 } { y }$

Question 54

Find the amount of pure ingredient needed to prepare the solution as indicated. 720 mL of 1 : 60 sodium bicarbonate solution from pure sodium bicarbonate

A) 9 mL
B) 12 mL
C) 11 mL
D) 43,200 mL
E) 17 mL

Question 55

A car is listed to sell at $22,600, the salesperson offers to sell it to you $17,100. What percent of the list price is the reduction? Round your answer to the nearest tenth of a percent if necessary.

A) 25.4%
B) 22.1%
C) 27.6%
D) 24.3%
E) 0.2%

Question 56

A plane flies 3 h and uses 45 gal of 100LL aviation fuel. How much will be used if the plane flew only 1.5 h?

A) 19.5 gallons
B) 22.5 gallons
C) 23.5 gallons
D) 67.5 gallons
E) 27.5 gallons

Question 57

A multiple-dose vial been mixed and labeled "200,000 units in 1 cm ³ ." How many cubic centimeters are needed to give 900,000 units?

A) 2.3 cm ³
B) 4.5 cm ³
C) 3.7 cm ³
D) 3.4 cm ³
E) 1.2 cm ³

Question 58

Find the amount (in mL) of pure ingredient needed to prepare the solution as indicated. Give the answer to one decimal place, if necessary.
200 mL of 9% Lysol solution from pure Lysol
__________ mL

Question 59

At the beginning of a trip, a tire on a car has a pressure of 35 psi (lb/in ² ). At the end of the trip, the pressure is 43 psi. What is the percent increase in pressure? Round your answer to the nearest tenth of a percent if necessary.

A) 21.8%
B) 20.7%
C) 26.2%
D) 22.9%
E) 0.2%

Question 60

Solve the proportion. Round the result to three significant digits if necessary. $\frac { x } { 32 } = \frac { 60 } { 84 }$

Question 61

Calculate the values of x and y in the following table.   $\begin{array} { | l | l | l | l | } \hline F _ { 1 } & d _ { 1 } & F _ { 2 } & d _ { 2 } \\\hline 16 \mathrm { lb } & 4 \text { in. } & 8 \mathrm { lb } & x \text { in. } \\\hline 110 \mathrm { lb } & y \text { in. } & 60 \mathrm { lb } & 11 \text { in. } \\\hline\end{array}$

A) x = 16, y = 10
B) x = 8, y = 6
C) x = 16, y = 5
D) x = 6, y = 5
E) x = 6, y = 10

Question 62

Calculate the values of x and y in the following table. $\begin{array} { | l | l | l | l | } \hline \text { Gear A } && \text { Gear B } \\\hline \begin{array} { l } \text { Number of } \\\text { teeth }\end{array} & \mathrm { rpm } & \begin{array} { l } \text { Number of } \\\text { teeth }\end{array} & \mathrm { rpm } \\\hline 40 & 700 & 25 & x \\\hline 50 & 56 & y & 80 \\\hline\end{array}$

A) x = 1,120, y = 35
B) x = 1,125, y = 72
C) x = 560, y = 35
D) x = 2,240, y = 72
E) x = 1,125, y = 36

Question 63

Draw a sketch for the problem and solve it. A piece of machinery weighs 5 tons. It is to be balanced by two men whose combined weight is 400 lb. The piece of machinery is placed 8 in. from the fulcrum. How far from the fulcrum must the two men exert their weight in order to balance it?

A) 23 in.
B) 460 in.
C) 230 in.
D) 200 in.
E) 198 in.

Question 64

A large pulley turns at 60 rpm. A smaller pulley 6 in. in diameter turns at 400 rpm. What is the diameter of the larger pulley?

A) 21.5 in.
B) 100 in.
C) 43 in.
D) 50 in.
E) 40 in.

Question 65

A large pulley turns at 105 rpm. A smaller pulley 7 in. in diameter turns at 300 rpm. What is the diameter of the larger pulley?
__________ inches

Question 66

A small pulley is 9 in. in diameter, and a larger one is 17 in. in diameter. How many rpm does the larger pulley make if the smaller one revolves at 850 rpm?
__________ rpm

Question 67

Calculate the values of x and y in the following table? $$\begin{array} { | l | l | l | l | } \hline \multicolumn{2}{|l|} { \text { Pulley A } } & \text { Pulley B } \\\hline \text { Diameter } & \mathrm { rpm } & \text { Diameter } & \mathrm { rpm } \\\hline 34 \mathrm {~cm} & 54 & 68 \mathrm {~cm} & x \\\hline 18 \mathrm {~cm} & y & 12 \mathrm {~cm} & 96 \\\hline\end{array}$$

A) x = 108, y = 32
B) x = 27, y = 64
C) x = 13.5, y = 64
D) x = 108, y = 64
E) x = 13.5, y = 32

Question 68

A large gear with 100 teeth turning at 210 rpm turns a small gear with 12 teeth. At how many rpm does the small gear turn?

A) 1,749 rpm
B) 1,790 rpm
C) 895 rpm
D) 3,580 rpm
E) 1,750 rpm

Question 69

Calculate the values of x and y in the following chart.  

$\begin{array}{l}\hline { \text { Pulley A } }\quad\quad\quad\quad\quad\quad \text { Pulley B } \\\begin{array}{ | l | l | l | l | } \hline \text { Diameter } & \mathrm { rpm } & \text { Diameter } & \mathrm { rpm } \\\hline 36 \mathrm {~cm} & 400 & x \mathrm {~cm} & 720 \\\hline 15 \mathrm {~cm} & 300 & 24 \mathrm {~cm} & y \\\hline\end{array}\end{array}$

A) x = 240, y = 1,885
B) x = 24, y = 188.5
C) x = 48, y = 375
D) x = 24, y = 375
E) x = 20, y = 187.5

Question 70

Draw a sketch for the problem and solve it. A rocker arm raises oil from an oil well. On each stroke, it lifts a weight of 3 tons on a weight arm 1 ft long. What force is needed to lift the oil on a force arm 2 ft long?

A) 0.75 ton
B) 3 tons
C) 6 tons
D) 12 tons
E) 1.5 tons

Question 71

One pulley is twice as large in diameter as a second pulley. If the larger pulley turns at 259 rpm, what is the rpm of the smaller?

A) 518 rpm
B) 129.5 rpm
C) 538 rpm
D) 1,076 rpm
E) 522 rpm

Question 72

Calculate the values of x and y in the following table.

$\begin{array}{l}\hline { \text { Pulley A } }\quad\quad\quad\quad\quad\quad \text { Pulley B } \\\begin{array}{ | l | l | l | l | } \hline \text { Diameter } & \text { rpm } & \text { Diameter } & \text { rpm } \\\hline x \text { in. } & 625 & 25 \text { in. } & 975 \\\hline 96 \mathrm {~cm} & 240 & y \mathrm {~cm} & 360 \\\hline\end{array}\end{array}$

A) x = 78, y = 122
B) x = 42, y = 61
C) x = 39, y = 64
D) x = 42, y = 122
E) x = 21, y = 61

Question 73

Calculate the values of x and y in the following table.   $\begin{array}{|l|l|l|l|}\hline \text { Gear A } & &\text { Gear B } \\\hline \begin{array}{l}\text { Number of } \\\text { teeth }\end{array} & \text { rpm } & \begin{array}{l}\text { Number of } \\\text { teeth }\end{array} & \mathrm{rpm} \\\hline 10 & 100 & x & 125 \\\hline 260 & y & 50 & 520 \\\hline\end{array}$

A) x = 8, y = 25
B) x = 2, y = 200
C) x = 8, y = 100
D) x = 16, y = 200
E) x = 16, y = 25

Question 74

Draw a sketch for the problem and solve it. An object is 4 ft from the fulcrum and balances a second object 8 ft from the fulcrum. The first object weighs 64 lb. How much does the second object weighs?

A) 32 lb
B) 37 lb
C) 128 lb
D) 64 lb
E) 42 lb

Question 75

A large gear with 300 teeth turning at 11 rpm turns a small gear at 150 rpm. How many teeth does the small gear have?

A) 5.5
B) 36
C) 27
D) 22
E) 72

Question 76

Calculate the values of x and y in the following table.   $\begin{array} { | l | l | l | l | } \hline F _ { 1 } & d _ { 1 } & F _ { 2 } & d _ { 2 } \\\hline 27 \mathrm { lb } & 6 \text { in. } & x \mathrm { lb } & 2 \mathrm { in. } \\\hline y \mathrm { lb } & 4.2 \mathrm { in } . & 512.6 \mathrm { lb } & 4.4 \mathrm { in } . \\\hline\end{array}$

A) x = 240, y = 537.0
B) x = 8.1, y = 5,370.1
C) x = 81, y = 537.0
D) x = 80, y = 537.0
E) x = 240, y = 1,074.0

Question 77

A small pulley is 13 in. in diameter, and a larger one is 19 in. in diameter. How many rpm does the larger pulley make if the smaller one revolves at 570 rpm?

A) 820 rpm
B) 833.0769230769 rpm
C) 410 rpm
D) 390 rpm
E) 380 rpm

Question 78

A large gear with 405 teeth running at 300 rpm turns a small gear 450 rpm. How many teeth does the small gear have?

A) 180
B) 540
C) 320
D) 267
E) 270

Question 79

Calculate the values of x and y in the following table.  

$\begin{array}{l}\hline { \text { Pulley A } }\quad\quad\quad\quad\quad\quad \text { Pulley B } \\\begin{array}{|l|l|}\hline \text { Diameter } & \mathrm{rpm} \\\hline 30 \mathrm{~cm} & 150 \\\hline y \text { in. } & 40 \\\hline\end{array}\begin{array}{l|l|}\hline \text { Diameter } & \mathrm{rpm} \\\hline 45 \mathrm{~cm} & x \\\hline 24 \mathrm{in} . & 20 \\\hline\end{array}\end{array}$

A) x = 200, y = 24
B) x = 100, y = 12
C) x = 50, y = 6
D) x = 300, y = 18
E) x = 50, y = 18

Question 80

A hydraulic pump is driven with an electric motor(see figure below). The pump must rotate at 1,000 rpm. The pump is equipped with a 6.0-in.-diameter belt pulley. The motor runs at 1,500 rpm. What diameter pulley is required on the motor?

A) 3 in.
B) 2 in.
C) 4 in.
D) 5 in.
E) 10 in.