Question 1

A cashier has a total of 132 bills, made up of fives and tens. The total value of the money is $880. How many ten-dollar bills does the cashier have?

Accepted Answer

A) 22 ten-dollar bills 
B) 66 ten-dollar bills 
C) 44 ten-dollar bills 
D) 88 ten-dollar bills 
A) 22 ten-dollar bills 
B) 66 ten-dollar bills 
C) 44 ten-dollar bills 
D) 88 ten-dollar bills

Question 2

If one step in the solution of an equation is -40 = -9, what is the final solution of the
equation?

Accepted Answer

The answer of If one step in the solution of...

Question 3

Solve the inequality, then graph the solution.
-$- 10 < 5 y \leq 10$

Accepted Answer

A)  $[ - 2,2 )$
  
B)  $( - 2,2 ]$
  
C)  $[ - 2,2 ]$
  
D)  $( - 2,2 )$
  
A)  $[ - 2,2 )$
  
B)  $( - 2,2 ]$
  
C)  $[ - 2,2 ]$
  
D)  $( - 2,2 )$

Question 4

Helen Weller invested $10,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the average return on
The two investments amounts to 13%?

Accepted Answer

A) $6000 
B) $10,000 
C) $5000 
D) $7000 
A) $6000 
B) $10,000 
C) $5000 
D) $7000

Question 5

The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. If $\mathrm { V } = 121.0$ in. ${ } ^ { 3 }$ when $\mathrm { T } = 110 ^ { \circ }$ and $\mathrm { P } = 10 \mathrm { lb } /$ in. 2 , what is the volume when $\mathrm { T } = 380 ^ { \circ }$ and $P = 15 \mathrm { lb } /$ in. $^ { 2 }$ ? (Round to the nearest tenth.)

Accepted Answer

A)  $278.7 \mathrm { in. } ^ { 3 }$ 
B)  $258.7 \mathrm { in. } ^ { 3 }$ 
C)  $318.7$ in. 3 
D)  $238.7 \mathrm { in. } ^ { 3 }$ 
A)  $278.7 \mathrm { in. } ^ { 3 }$ 
B)  $258.7 \mathrm { in. } ^ { 3 }$ 
C)  $318.7$ in. 3 
D)  $238.7 \mathrm { in. } ^ { 3 }$

Question 6

Solve the formula for the specified variable.
-$P = s _ { 1 } + s _ { 2 } + s _ { 3 } ;$ for $s _ { 3 }$

Accepted Answer

A)  $s _ { 3 } = s _ { 1 } + s _ { 2 } - P$ 
B)  $s _ { 3 } = P - s _ { 1 } - s _ { 2 }$ 
C)  $s _ { 3 } = P + s _ { 1 } + s _ { 2 }$ 
D)  $s _ { 3 } = s _ { 1 } + P - s _ { 2 }$ 
A)  $s _ { 3 } = s _ { 1 } + s _ { 2 } - P$ 
B)  $s _ { 3 } = P - s _ { 1 } - s _ { 2 }$ 
C)  $s _ { 3 } = P + s _ { 1 } + s _ { 2 }$ 
D)  $s _ { 3 } = s _ { 1 } + P - s _ { 2 }$

Question 7

Solve the problem.
-The ratio of the lengths of strings that play the notes D and B is 27 to 16. If a string 64 cm long plays a B, what is the length of the string that plays a D?

Accepted Answer

A) 108 cm 
B) 91 cm 
C) 64 cm 
D) 80 cm 
A) 108 cm 
B) 91 cm 
C) 64 cm 
D) 80 cm

Question 8

Let x represent the unknown, and write an equation for the sentence. Do not solve.
-When 90% of a number is subtracted from 30, the result is 7 less than the number.

Accepted Answer

A) 30 - 90x = x - 7 
B) 0.9x - 30 = x - 7 
C) 30 - 0.9x = 7 - x 
D) 30 - 0.9x = x - 7 
A) 30 - 90x = x - 7 
B) 0.9x - 30 = x - 7 
C) 30 - 0.9x = 7 - x 
D) 30 - 0.9x = x - 7

Question 9

Roberto invested some money at 7%, and then invested $2000 more than twice this amount at 10%. His total annual income from the interest was $3710. How much was invested at 10%?

Accepted Answer

A) $2800 
B) $26,000 
C) $6000 
D) $28,000 
A) $2800 
B) $26,000 
C) $6000 
D) $28,000

Question 10

Solve the equation.
-$\frac { 3 r - 2 } { r } = \frac { 6 } { 9 }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 7 } { 6 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 6 } { 7 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 7 } { 6 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 6 } { 7 }$

Question 11

Determine the ratio and write it in lowest terms.
-120 cm to 45 cm

Accepted Answer

A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 46 } { 121 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $\frac { 121 } { 46 }$ 
A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 46 } { 121 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $\frac { 121 } { 46 }$

Question 12

Match the inequality with its correct representation.
-$\{ x \mid - 7 < x < 9 \}$

Accepted Answer

A)  $[ - 7,9 )$ 
B)  $( - 7,9 )$ 
C)  $[ - 7,9 ]$ 
D)  $( - 7,9 ]$ 
A)  $[ - 7,9 )$ 
B)  $( - 7,9 )$ 
C)  $[ - 7,9 ]$ 
D)  $( - 7,9 ]$

Question 13

Match the inequality with its correct representation.
-

Accepted Answer

A) $x \geq 7$ B) $x > 7$ C) $x < 7$ D) $x \leq 7$ A) $x \geq 7$ B) $x > 7$ C) $x < 7$ D) $x \leq 7$

Question 14

Solve the problem.
-If 2 hours are required to type 10 pages, how many hours would be required to type 30 pages?

Accepted Answer

A) 2 hours 
B) 5 hours 
C) 4 hours 
D) 6 hours 
A) 2 hours 
B) 5 hours 
C) 4 hours 
D) 6 hours

Question 15

Solve the problem.
-If a boat uses 17 gallons of gas to go 66 miles, how many miles can the boat travel on 51 gallons of gas?

Accepted Answer

A) 396 miles 
B) 198 miles 
C) 22 miles 
D) 218 miles 
A) 396 miles 
B) 198 miles 
C) 22 miles 
D) 218 miles

Question 16

Solve the problem.
-Find the missing length in the similar triangles.

Accepted Answer

A)  x = 12 
B)  x = 25 
C)  x = 20 
D)  x= 19 
A)  x = 12 
B)  x = 25 
C)  x = 20 
D)  x= 19

Question 17

Solve the inequality. Give the solution set in interval form and graph the interval.
-$15 ( 3 x - 13 ) > 3 ( 15 x - 8 )$

Accepted Answer

A)  $( - \infty , 0 )$
  
B)  $( \infty , \infty )$
  
C)  $\varnothing$
  
D)  $( 0 , \infty )$
  
A)  $( - \infty , 0 )$
  
B)  $( \infty , \infty )$
  
C)  $\varnothing$
  
D)  $( 0 , \infty )$

Question 18

Answer the question based on the given graph.
-  
In which month(s)is the percentage of earthquakes at most 5.1%?

Accepted Answer

A) January and March 
B) March and September 
C) March 
D) January and September 
A) January and March 
B) March and September 
C) March 
D) January and September

Question 19

Gloria collected 29 fantail and comet goldfish. There were 5 fewer fantails than comets. How many comets did Gloria have?

Accepted Answer

A) 24 comets 
B) 11 comets 
C) 12 comets 
D) 17 comets 
A) 24 comets 
B) 11 comets 
C) 12 comets 
D) 17 comets

Question 20

Solve the problem.
-The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1970.

Accepted Answer

A) 1950 
B) 1825 
C) 1900 
D) 1850 
A) 1950 
B) 1825 
C) 1900 
D) 1850

A cashier has a total of 132 bills, made up of fives and tens. The total value of the money is $880. How many ten-dollar bills does the cashier have?

If one step in the solution of an equation is -40 = -9, what is the final solution of the equation?

Solve the inequality, then graph the solution. - $- 10 < 5 y \leq 10$ $Solve the inequality, then graph the solution. - - 10 < 5 y \leq 10$

Helen Weller invested $10,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the average return on The two investments amounts to 13%?

Solve the formula for the specified variable. - $P = s _ { 1 } + s _ { 2 } + s _ { 3 } ;$ for $s _ { 3 }$

Solve the problem. -The ratio of the lengths of strings that play the notes D and B is 27 to 16. If a string 64 cm long plays a B, what is the length of the string that plays a D?

Let x represent the unknown, and write an equation for the sentence. Do not solve. -When 90% of a number is subtracted from 30, the result is 7 less than the number.

Roberto invested some money at 7%, and then invested $2000 more than twice this amount at 10%. His total annual income from the interest was $3710. How much was invested at 10%?

Solve the equation. - $\frac { 3 r - 2 } { r } = \frac { 6 } { 9 }$

Determine the ratio and write it in lowest terms. -120 cm to 45 cm

Match the inequality with its correct representation. - $\{ x \mid - 7 < x < 9 \}$

Match the inequality with its correct representation. -

Solve the problem. -If 2 hours are required to type 10 pages, how many hours would be required to type 30 pages?

Solve the problem. -If a boat uses 17 gallons of gas to go 66 miles, how many miles can the boat travel on 51 gallons of gas?

Solve the problem. -Find the missing length in the similar triangles.

Solve the inequality. Give the solution set in interval form and graph the interval. - $15 ( 3 x - 13 ) > 3 ( 15 x - 8 )$

Answer the question based on the given graph. - In which month(s)is the percentage of earthquakes at most 5.1%?

Gloria collected 29 fantail and comet goldfish. There were 5 fewer fantails than comets. How many comets did Gloria have?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 7: The Basic Concepts of Algebra

A cashier has a total of 132 bills, made up of fives and tens. The total value of the money is $880. How many ten-dollar bills does the cashier have?

If one step in the solution of an equation is -40 = -9, what is the final solution of the equation?

Solve the inequality, then graph the solution. - −10<5y≤10- 10 < 5 y \leq 10−10<5y≤10

Helen Weller invested $10,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the average return on The two investments amounts to 13%?

Solve the formula for the specified variable. - P=s1+s2+s3;P = s _ { 1 } + s _ { 2 } + s _ { 3 } ;P=s1​+s2​+s3​; for s3s _ { 3 }s3​

Solve the problem. -The ratio of the lengths of strings that play the notes D and B is 27 to 16. If a string 64 cm long plays a B, what is the length of the string that plays a D?

Let x represent the unknown, and write an equation for the sentence. Do not solve. -When 90% of a number is subtracted from 30, the result is 7 less than the number.

Roberto invested some money at 7%, and then invested $2000 more than twice this amount at 10%. His total annual income from the interest was $3710. How much was invested at 10%?

Solve the equation. - 3r−2r=69\frac { 3 r - 2 } { r } = \frac { 6 } { 9 }r3r−2​=96​

Determine the ratio and write it in lowest terms. -120 cm to 45 cm

Match the inequality with its correct representation. - {x∣−7<x<9}\{ x \mid - 7 < x < 9 \}{x∣−7<x<9}

Match the inequality with its correct representation. -

Solve the problem. -If 2 hours are required to type 10 pages, how many hours would be required to type 30 pages?

Solve the problem. -If a boat uses 17 gallons of gas to go 66 miles, how many miles can the boat travel on 51 gallons of gas?

Solve the problem. -Find the missing length in the similar triangles.

Solve the inequality. Give the solution set in interval form and graph the interval. - 15(3x−13)>3(15x−8)15 ( 3 x - 13 ) > 3 ( 15 x - 8 )15(3x−13)>3(15x−8)

Answer the question based on the given graph. - In which month(s)is the percentage of earthquakes at most 5.1%?

Gloria collected 29 fantail and comet goldfish. There were 5 fewer fantails than comets. How many comets did Gloria have?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Solve the inequality, then graph the solution. - $- 10 < 5 y \leq 10$ $Solve the inequality, then graph the solution. - - 10 < 5 y \leq 10$

Solve the formula for the specified variable. - $P = s _ { 1 } + s _ { 2 } + s _ { 3 } ;$ for $s _ { 3 }$

Solve the equation. - $\frac { 3 r - 2 } { r } = \frac { 6 } { 9 }$

Match the inequality with its correct representation. - $\{ x \mid - 7 < x < 9 \}$

Solve the inequality. Give the solution set in interval form and graph the interval. - $15 ( 3 x - 13 ) > 3 ( 15 x - 8 )$