Question 1

Use the properties of equality to solve the equation. $$\frac { 11 } { 12 } a = \frac { 1 } { 3 }$$
A) $a = \frac { 1 } { 12 }$
B) $a = \frac { 4 } { 11 }$
C) $a = \frac { 1 } { 11 }$
D) $a = \frac { 4 } { 3 }$
E)none of these

Accepted Answer

B

Question 2

Solve the equation. $$2 x + 4 + 7 x = 3 x + 2 x - 32$$
A)x = -9
B)x = -7
C)x = -13
D)x = 13
E)x = -5

Accepted Answer

Combining like terms on both sides gives $9x + 4 = 5x - 32$. Subtracting $5x$ and $4$ from both sides gives $4x = -36$, so $x = -9$.

Question 3

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3
A)t = -36
B)t = 108
C)t = 36
D)t = 72
E)t = 34

Accepted Answer

To solve for t, we need to get all the t terms on one side and all the constant terms on the other side.

0.11 t - 2.1 = 0.06 t - 0.3

First, let's get rid of the decimal points by multiplying everything by 100:

11t - 210 = 6t - 30

Next, let's isolate the t terms:

11t - 6t = 210 - 30

5t = 180

Finally, let's solve for t:

t = 36

Therefore, the solution is t = 36, which is choice C.

Question 4

Solve the equation. n + 0.5 n = 90
A)n = 90
B)n = 0.5
C)n = -29.5
D)n = 60
E)n = 149.5

Accepted Answer

Combining like terms on the left side of the equation, we get 1.5n = 90.
Dividing both sides by 1.5, we get n = 60. Therefore, the answer is D, n = 60.

Question 5

Use a property of equality to solve the equation. $$\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$$
A) $5$
B) $7$.
C) $2$
D) $7$
E) $0$

Accepted Answer

To solve for $x$, add $\frac{17}{3}$ to both sides of the equation: $\frac{4}{3} + \frac{17}{3} = x$, which simplifies to $\frac{21}{3} = x$, or $7 = x$.

Question 6

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ". 
A)x = 11
B)x = 15
C)x = 6
D)x = 8
E)x = 10

Accepted Answer

Since $\angle 1$ and $\angle 3$ are vertical angles, they have the same measure. Setting the two expressions for their measures equal to each other and solving for x, we get: 
$$(5x + 10)^\circ = (7x - 10)^\circ$$
$$5x + 10 = 7x - 10$$
$$20 = 2x$$
$$x = 10$$
Therefore, the answer is choice E.

Question 7

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?
A)2%
B)6%
C)8%
D)5%
E)3%

Accepted Answer

The sales tax rate can be found by dividing the tax amount by the price of the item and then converting it to a percentage. So, $0.84 / $14 = 0.06, which is 6% when converted to a percentage.

Question 8

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4)= 2( x + 5)
A) $x = - \frac { 9 } { 2 }$
B) $x = \frac { 11 } { 2 }$
C) $x = \frac { 5 } { 2 }$
D)identity
E)contradiction

Accepted Answer

The answer of Solve the equation. If the equation is...

Question 9

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.
A)15
B)30
C)25
D)35
E)20

Accepted Answer

The answer of Use an algebraic approach to solve the...

Question 10

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal)of $4,250 has grown to be $4,520?
A)$280
B)$270
C)$255
D)$275
E)$250

Accepted Answer

The interest earned is calculated by subtracting the original principal from the total amount after interest has been added. So, $4,520 - $4,250 = $270.

Question 11

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?
A)$2,500 at 13%, $5,000 at 15%
B)$5,000 at 13%, $7,500 at 15%
C)$5,200 at 13%, $7,300 at 15%
D)$5,200 at 13%, $7,700 at 15%
E)$7,500 at 13%, $5,000 at 15%

Accepted Answer

Let the amount invested at 13% be x dollars. Then, the amount invested at 15% is x + $2,500. The total interest from both investments is $1,775, which can be represented by the equation: 0.13x + 0.15(x + 2500) = 1775. Solving this equation gives x = $5,000 for the 13% investment and x + $2,500 = $7,500 for the 15% investment.

Question 12

Solve the equation. 0.43 x + 0.4(8,000 - x )= 3350
A)x = 5,000
B)x = 3,000
C)x = -3,000
D)x = 8,000
E)no solution

Accepted Answer

To solve the equation, distribute and simplify: 0.43x + 0.4(8000 - x) = 3350. This simplifies to 0.43x + 3200 - 0.4x = 3350. Combining like terms gives 0.03x = 150. Dividing both sides by 0.03 gives x = 5000.

Question 13

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$
A) $p = \frac { 2 } { 5 }$
B) $p = \frac { 1 } { 15 }$
C) $p = 1 \frac { 4 } { 15 }$
D) $p = \frac { 11 } { 15 }$
E)none of these

Accepted Answer

To solve for $p$, add $\frac{2}{5}$ to both sides of the equation to isolate $p$: $p = \frac{1}{3} + \frac{2}{5}$. Finding a common denominator (15) for the fractions gives $p = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.

Question 14

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$
A) $h = \frac { 8 } { 15 }$
B) $h = \frac { 15 } { 56 }$
C) $h = \frac { 1 } { 15 }$
D) $h = \frac { 56 } { 15 }$
E)no solution

Accepted Answer

To solve the equation, we first need to find a common denominator for the two fractions. The smallest common multiple of 7 and 8 is 56. Therefore, we can rewrite the equation as:

\begin{align*}
\frac{h}{7}+\frac{h}{8}&=1\
\frac{8h}{56}+\frac{7h}{56}&=1\
\frac{15h}{56}&=1\
15h&=56\
h&=\frac{56}{15}\
\end{align*}

Therefore, the answer is D.

Question 15

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.
A)5 inches wide, 7 inches long
B)2 inches wide, 10 inches long
C)3 inches wide, 9 inches long
D)4 inches wide, 8 inches long
E)7 inches wide, 5 inches long

Accepted Answer

The perimeter of a rectangle is given by $2l + 2w = 24$, where $l$ is the length and $w$ is the width. Given $w = \frac{1}{4}l + 2$, substituting the width's expression into the perimeter equation gives $2l + 2(\frac{1}{4}l + 2) = 24$. Solving this equation for $l$ gives $l = 8$ inches. Substituting $l = 8$ inches back into $w = \frac{1}{4}l + 2$ gives $w = 4$ inches. Therefore, the rectangle is 4 inches wide and 8 inches long.

Question 16

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.
A)20 feet
B)4 feet
C)12 feet
D)-4 feet
E)8 feet

Accepted Answer

Let the length of the shorter piece be $x$ feet. Then, the length of the longer piece is $\frac{2}{3}x$ feet. Since the total length of the board is 20 feet, we have $x + \frac{2}{3}x = 20$. Solving for $x$, we find that $x = 8$ feet, making the shorter piece 8 feet long.

Question 17

Use a property of equality to solve the equation. $$\frac { y } { 18 } = - 8$$
A)-147
B)- 152
C)- 153
D)- 137
E)- 144

Accepted Answer

To solve the equation $\frac{y}{18} = -8$, use the multiplication property of equality by multiplying both sides by 18 to isolate $y$. This gives $y = 18 \times -8 = -144$.

Question 18

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?
A)$64,500
B)$69,500
C)$68,500
D)$67,500
E)$71,500

Accepted Answer

The answer of Use an equation to solve the problem....

Question 19

Solve the equation. 5( t - 2)+ 2( t - 1)= -2( t - 1)+ 10( t + 2)
A)t = -44
B)t = -36
C)t = -34
D)t = -29
E)t = -27

Accepted Answer

First, distribute the numbers in the equation: 5(t - 2) + 2(t - 1) = -2(t - 1) + 10(t + 2) becomes 5t - 10 + 2t - 2 = -2t + 2 + 10t + 20. Simplify both sides: 7t - 12 = 8t + 22. Rearrange to solve for t: 7t - 8t = 22 + 12, which simplifies to -t = 34, so t = -34.

Question 20

Solve the equation. $$7 x - 15 + 6 x - 10 x + 9 = 24$$
A)x = 11
B)x = -10
C)x = 3
D)x = 10
E)x = 20

Accepted Answer

The answer of Solve the equation. \[7 x - 15...

Quiz 2: Equations, Inequalities, and Problem Solving

Use the properties of equality to solve the equation. $\frac { 11 } { 12 } a = \frac { 1 } { 3 }$

Solve the equation. $2 x + 4 + 7 x = 3 x + 2 x - 32$

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Solve the equation. n + 0.5 n = 90

Use a property of equality to solve the equation. $\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4) = 2( x + 5)

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,250 has grown to be $4,520?

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Solve the equation. 0.43 x + 0.4(8,000 - x ) = 3350

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

Use a property of equality to solve the equation. $\frac { y } { 18 } = - 8$

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Solve the equation. 5( t - 2) + 2( t - 1) = -2( t - 1) + 10( t + 2)

Solve the equation. $7 x - 15 + 6 x - 10 x + 9 = 24$