Question 1

Solve the problem.
-A sum of money amounting to $\$ 3.45$ consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

Accepted Answer

A)  16 quarters 
B)  7 quarters 
C)  11 quarters 
D)  9 quarters 
A)  16 quarters 
B)  7 quarters 
C)  11 quarters 
D)  9 quarters

Question 2

Solve the problem using the elimination method.
-The sum of two numbers is 4 . Three times the larger number plus two times the smaller number is 37 . Find the numbers.

Accepted Answer

A)  25 and $- 21$ 
B)  33 and $- 29$ 
C)  29 and $- 25$ 
D)  25 and $- 29$ 
A)  25 and $- 21$ 
B)  33 and $- 29$ 
C)  29 and $- 25$ 
D)  25 and $- 29$

Question 3

Solve using the elimination method.
-$x + y = 11$ $x - y = 7$

Accepted Answer

A)  No solution 
B)  $( 9,2 )$ 
C)  $( 8,3 )$ 
D)  $( - 9,3 )$ 
A)  No solution 
B)  $( 9,2 )$ 
C)  $( 8,3 )$ 
D)  $( - 9,3 )$

Question 4

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
2 x - 4 y = 2 \
y = \frac { 1 } { 2 } x - \frac { 1 } { 2 }
\end{array}$$

Accepted Answer

A)  Consistent and dependent 
B)  Consistent and independent 
C)  Inconsistent and dependent 
D)  Inconsistent and independent 
A)  Consistent and dependent 
B)  Consistent and independent 
C)  Inconsistent and dependent 
D)  Inconsistent and independent

Question 5

Solve the system of equations by the elimination method.
-$$\begin{array} { r } 
0.3 x + 0.5 y = 3.1 \
x - 0.1 y = 1.5
\end{array}$$

Accepted Answer

A)  $( 0.2,0.5 )$ 
B)  $( 5,2 )$ 
C)  no solution 
D)  $( 2,5 )$ 
A)  $( 0.2,0.5 )$ 
B)  $( 5,2 )$ 
C)  no solution 
D)  $( 2,5 )$

Question 6

Solve the problem.
-There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

Accepted Answer

A) 320 adults and 350 children 
B) 255 adults and 415 children 
C) 350 adults and 320 children 
D) 160 adults and 510 children 
A) 320 adults and 350 children 
B) 255 adults and 415 children 
C) 350 adults and 320 children 
D) 160 adults and 510 children

Question 7

Solve graphically.
-$\begin{array} { l } 
2 x + y = - 2 \
2 x + 2 y = 4
\end{array}$

Accepted Answer

A)  $( 4,6 )$ 
B)  $( - 4,6 )$ 
C)  $( 2 , - 6 )$ 
D)  $( - 4 , - 5 )$ 
A)  $( 4,6 )$ 
B)  $( - 4,6 )$ 
C)  $( 2 , - 6 )$ 
D)  $( - 4 , - 5 )$

Question 8

Solve by the substitution method.
-$$\begin{array} { l } 
6 x + 9 y = 114 \
4 x - 4 y = - 4
\end{array}$$

Accepted Answer

A)  No solution 
B)  $( 7,9 )$ 
C)  $( 6,9 )$ 
D)  $( 7,8 )$ 
A)  No solution 
B)  $( 7,9 )$ 
C)  $( 6,9 )$ 
D)  $( 7,8 )$

Question 9

Solve the system of equations by the elimination method.
-$- 0.8 x + 0.4 y = 4.8$ $0.1 x - 0.1 y = - 0.7$

Accepted Answer

A)  $( - 50,20 )$ 
B)  $( - 0.5,0.2 )$ 
C)  $( - 5,2 )$ 
D)  $( 2 , - 5 )$ 
A)  $( - 50,20 )$ 
B)  $( - 0.5,0.2 )$ 
C)  $( - 5,2 )$ 
D)  $( 2 , - 5 )$

Question 10

Solve.
-A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $21 \mathrm { mph }$, what is the speed of the plane in still air?

Accepted Answer

A)  $256 \mathrm { mph }$ 
B)  $236 \mathrm { mph }$ 
C)  $231 \mathrm { mph }$ 
D)  $221 \mathrm { mph }$ 
A)  $256 \mathrm { mph }$ 
B)  $236 \mathrm { mph }$ 
C)  $231 \mathrm { mph }$ 
D)  $221 \mathrm { mph }$

Question 11

Solve the system of equations by the elimination method.
-$\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21$
$\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7$

Accepted Answer

A)  $( - 12,9 )$ 
B)  $( 12,9 )$ 
C)  $( - 12 , - 9 )$ 
D)  $( 9 , - 12 )$ 
A)  $( - 12,9 )$ 
B)  $( 12,9 )$ 
C)  $( - 12 , - 9 )$ 
D)  $( 9 , - 12 )$

Question 12

Solve the problem.
-In a chemistry class, 6 liters of a $4 \%$ silver iodide solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

Accepted Answer

A)  $4.0 \mathrm {~L}$ 
B)  $3.0 \mathrm {~L}$ 
C)  $2.0 \mathrm {~L}$ 
D)  $6.0 \mathrm {~L}$ 
A)  $4.0 \mathrm {~L}$ 
B)  $3.0 \mathrm {~L}$ 
C)  $2.0 \mathrm {~L}$ 
D)  $6.0 \mathrm {~L}$

Question 13

Solve.
-An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Accepted Answer

A)  $400 \mathrm { mph }$ 
B)  $200 \mathrm { mph }$ 
C)  $300 \mathrm { mph }$ 
D)  $100 \mathrm { mph }$ 
A)  $400 \mathrm { mph }$ 
B)  $200 \mathrm { mph }$ 
C)  $300 \mathrm { mph }$ 
D)  $100 \mathrm { mph }$

Question 14

Solve the problem using the elimination method.
-In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

Accepted Answer

A)  two-point shots: 11 ; three-point shots: 6 
B)  two-point shots: 6; three-point shots: 11 
C)  two-point shots: 10 ; three-point shots: 7 
D)  two-point shots: 12; three-point shots: 5 
A)  two-point shots: 11 ; three-point shots: 6 
B)  two-point shots: 6; three-point shots: 11 
C)  two-point shots: 10 ; three-point shots: 7 
D)  two-point shots: 12; three-point shots: 5

Question 15

Solve the problem using the elimination method.
-There were 490 people at a play. The admission price was $\$ 3$ for adults and $\$ 1$ for children. The admission receipts were $\$ 1070$. How many adults and how many children attended?

Accepted Answer

A)  290 adults and 200 children 
B)  267 adults and 223 children 
C)  100 adults and 390 children 
D)  200 adults and 290 children 
A)  290 adults and 200 children 
B)  267 adults and 223 children 
C)  100 adults and 390 children 
D)  200 adults and 290 children

Question 16

Solve the problem.
-The perimeter of a triangle is $65 \mathrm {~cm}$. The triangle is isosceles now, but if its base were lengthened by $6 \mathrm {~cm}$ and each leg were shortened by $7 \mathrm {~cm}$, it would be equilateral. Find the base of the original triangle.

Accepted Answer

A)  $19 \mathrm {~cm}$ 
B)  $26 \mathrm {~cm}$ 
C)  $13 \mathrm {~cm}$ 
D)  $12 \mathrm {~cm}$ 
A)  $19 \mathrm {~cm}$ 
B)  $26 \mathrm {~cm}$ 
C)  $13 \mathrm {~cm}$ 
D)  $12 \mathrm {~cm}$

Question 17

Solve using the elimination method.
-$$\begin{array} { l } 
4 x - y = 19 \
5 x + y = 35
\end{array}$$

Accepted Answer

A)  $( 5,6 )$ 
B)  $( 6,5 )$ 
C)  $( 6,6 )$ 
D)  No solution 
A)  $( 5,6 )$ 
B)  $( 6,5 )$ 
C)  $( 6,6 )$ 
D)  No solution

Question 18

Solve.
-The speed of a stream is $6 \mathrm { mph }$. If a boat travels 68 miles downstream in the same time that it takes to travel 34 miles upstream, what is the speed of the boat in still water?

Accepted Answer

A)  $12 \mathrm { mph }$ 
B)  $18 \mathrm { mph }$ 
C)  $21 \mathrm { mph }$ 
D)  $20 \mathrm { mph }$ 
A)  $12 \mathrm { mph }$ 
B)  $18 \mathrm { mph }$ 
C)  $21 \mathrm { mph }$ 
D)  $20 \mathrm { mph }$

Question 19

Solve by the substitution method.
-$$\begin{array} { l } 
x + 6 y = - 1 \
7 x + 7 y = - 7
\end{array}$$

Accepted Answer

A)  $( - 1,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( 1 , - 1 )$ 
D)  No solution 
A)  $( - 1,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( 1 , - 1 )$ 
D)  No solution

Question 20

Solve the problem.
-The sum of two angles is $225 ^ { \circ }$. One angle is $30 ^ { \circ }$ less than twice the other. Find the angles.

Accepted Answer

A)  $136 ^ { \circ }$ and $89 ^ { \circ }$ 
B)  $85 ^ { \circ }$ and $140 ^ { \circ }$ 
C)  $83 ^ { \circ }$ and $142 ^ { \circ }$ 
D)  $83 ^ { \circ }$ and $136 ^ { \circ }$ 
A)  $136 ^ { \circ }$ and $89 ^ { \circ }$ 
B)  $85 ^ { \circ }$ and $140 ^ { \circ }$ 
C)  $83 ^ { \circ }$ and $142 ^ { \circ }$ 
D)  $83 ^ { \circ }$ and $136 ^ { \circ }$

Solve the problem. -A sum of money amounting to $\$ 3.45$ consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

Solve the problem using the elimination method. -The sum of two numbers is 4 . Three times the larger number plus two times the smaller number is 37 . Find the numbers.

Solve using the elimination method. - $x + y = 11$ $x - y = 7$

Classify the system as consistent or inconsistent, and dependent or independent. - 2x-4y=2 y=x-

Solve the system of equations by the elimination method. - 0.3x+0.5y=3.1 x-0.1y=1.5

Solve the problem. -There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

Solve graphically. - 2x+y=-2 2x+2y=4 $Solve graphically. - \begin{array} { l } 2 x + y = - 2 \\ 2 x + 2 y = 4 \end{array}$

Solve by the substitution method. - 6x+9y=114 4x-4y=-4

Solve the system of equations by the elimination method. - $- 0.8 x + 0.4 y = 4.8$ $0.1 x - 0.1 y = - 0.7$

Solve. -A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $21 \mathrm { mph }$ , what is the speed of the plane in still air?

Solve the system of equations by the elimination method. - $\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21$ $\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7$

Solve the problem. -In a chemistry class, 6 liters of a $4 \%$ silver iodide solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

Solve. -An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Solve the problem using the elimination method. -In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

Solve the problem using the elimination method. -There were 490 people at a play. The admission price was $\$ 3$ for adults and $\$ 1$ for children. The admission receipts were $\$ 1070$ . How many adults and how many children attended?

Solve the problem. -The perimeter of a triangle is $65 \mathrm {~cm}$ . The triangle is isosceles now, but if its base were lengthened by $6 \mathrm {~cm}$ and each leg were shortened by $7 \mathrm {~cm}$ , it would be equilateral. Find the base of the original triangle.

Solve using the elimination method. - 4x-y=19 5x+y=35

Solve. -The speed of a stream is $6 \mathrm { mph }$ . If a boat travels 68 miles downstream in the same time that it takes to travel 34 miles upstream, what is the speed of the boat in still water?

Solve by the substitution method. - x+6y=-1 7x+7y=-7

Solve the problem. -The sum of two angles is $225 ^ { \circ }$ . One angle is $30 ^ { \circ }$ less than twice the other. Find the angles.

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

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Exam 8: Systems of Equations

Solve the problem. -A sum of money amounting to $3.45\$ 3.45$3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?