Question 1

Solve.
-Angle A and angle B are supplementary angles and angle  A is $35 ^ { \circ }$ less than four times angle  B . Find the measures of angle  A  and angle  B .
$\text { Supplementary Angles }$

A) $\mathrm { A } = 151 ^ { \circ } , \mathrm { B } = 29 ^ { \circ }$
B) $\mathrm { A } = 131.7 ^ { \circ } , \mathrm { B } = 48.3 ^ { \circ }$
C) $\mathrm { A } = 137 ^ { \circ } , \mathrm { B } = 43 ^ { \circ }$
D) $A = 172 ^ { \circ } , B = 8 ^ { \circ }$

Accepted Answer

The answer of Solve.
-Angle A and angle B are supplementary...

Question 2

Solve.
-A region consists of 2565 thousand acres of farm land. If  30 %  of this land is privately owned, find how may acres are not privately owned.
A)  1795.5  thousand acres
B)  769.5  thousand acres
C)  1795.5  acres
D)  769.5  acres

Accepted Answer

The amount of land not privately owned is 70% of the total, so $2565 \times 0.7 = 1795.5$ thousand acres.

Question 3

Solve the equation for the specified variable.
- d=rt  for  r 
A) $r = \frac { d } { t }$
B) $r = \frac { t } { d }$
C)  r=dt
D)  r=d-t

Accepted Answer

To solve for $r$, divide both sides of the equation $d=rt$ by $t$, resulting in $r = \frac{d}{t}$.

Question 4

Solve.
-A Promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per munite for all calls. if joe's phone bill was $62 under this promotional deal, how many minuts of phone calls did he make? Round to the nearest interher, if necessary .
A) 9
B) 1540
C) 2
D) 940

Accepted Answer

Joe's phone bill minus the basic fee is $62 - $15 = $47. At $0.05 per minute, the number of minutes is $47 / $0.05 = 940.

Question 5

Solve.
-Find the measures of the angles of a triangle if the measure of the first angle is four times the measure of the second angle and the third angle is $30 ^ { \circ }$ more than the second angle.
A) $100 ^ { \circ } , 25 ^ { \circ } , 55 ^ { \circ }$
B) $35 ^ { \circ } , 5 ^ { \circ } , 140 ^ { \circ }$
C) $68 ^ { \circ } , 17 ^ { \circ } , 95 ^ { \circ }$
D) $20 ^ { \circ } , 5 ^ { \circ } , 155 ^ { \circ }$

Accepted Answer

The sum of the angles in a triangle is $180^\circ$. Let the measure of the second angle be $x$. Then, the first angle is $4x$ and the third angle is $x + 30^\circ$. The equation is $4x + x + (x + 30^\circ) = 180^\circ$, simplifying to $6x + 30^\circ = 180^\circ$, and solving for $x$ gives $x = 25^\circ$. Thus, the angles are $100^\circ, 25^\circ, 55^\circ$.

Question 6

Solve.
-The three most prominent buildings in a city, Washington Center, Lincoln Galleria, and Jefferson Square Tower, have a total height of 1800 feet. Find the height of each building if Jefferson Square Tower is three times as tall as Lincoln Galleria and Washington Center is 350 feet taller than Lincoln Galleria.
A) Washington Center: 240 feet
Lincoln Galleria: 80 feet 
Jefferson Square Tower: 1480 feet
B) Washington Center: 430 feet
 Lincoln Galleria: 80 feet
 Jefferson Square Tower: 1290 feet
C) Washington Center: 640 feet
630 feet Lincoln Galleria: 290 feet
Jefferson Square Tower: 870 
D) Washington Center: 630 feet
 Lincoln Galleria: 210
 Jefferson Square Tower: 960 feet

Accepted Answer

The answer of Solve.
-The three most prominent buildings in a...

Question 7

Solve.
-In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 81 and the U.S. won more than China who won more than Romania, how many medals did each team win?
A) U.S.: 29 medals; China: 28 medals; Romania: 27 medals
B) U.S.: 83 medals; China: 82 medals; Romania: 81 medals
C) U.S.: 28 medals; China: 27 medals; Romania: 26 medals
D) U.S.: 26 medals; China: 25 medals; Romania: 24 medals

Accepted Answer

The sum of three consecutive integers is 81. Let the integers be x, x+1, and x+2. Solving x + (x+1) + (x+2) = 81 gives x = 26. Therefore, the integers are 26, 27, and 28. The U.S. won 28, China 27, and Romania 26.

Question 8

Solve the equation for the specified variable.
-I= Prt  for  P
A) $P = \frac { \mathbf { r } - 1 } { \mathrm { It } }$.
B)  P=r - It 
C) $P = \frac { r - I } { 1 + t }$
D) $P = \frac { I } { r t }$

Accepted Answer

To solve for $P$, you need to isolate $P$ on one side of the equation. Starting with $I = Prt$, divide both sides by $rt$ to get $P = \frac{I}{rt}$.

Question 9

Solve.
-The president of a certain University makes three times as much money as one of the department heads. If the total of there salaries is $250,000 , find each worker's salary.
A) President salary =$18,750; department heads salary =$6250
B) President salary =$187,500; department heads salary =$62,500
C) President salary =$125,000; department heads salary =$62,500
D) President salary =$62,500; department heads salary =$187,500

Accepted Answer

Let the department head's salary be x. Then, the president's salary is 3x. The total salary is x + 3x = 4x = $250,000. Solving for x gives x = $62,500 (department head's salary). Therefore, the president's salary is 3x = $187,500.

Question 10

Solve.
-Angle A and angle B are complementary angles and angle A  is $2 ^ { \circ }$ more than three times angle  B . Find the measures of angle  A and angle  B .
$\text { Complemenatry Angles }\

A) \(\mathrm { A } = 48 ^ { \circ } , \mathrm { B } = 42 ^ { \circ }$
B) $\mathrm { A } = 68 ^ { \circ } , \mathrm { B } = 22 ^ { \circ }$
C) $\mathrm { A } = 42 ^ { \circ } , \mathrm { B } = 48 ^ { \circ }$
D) $\mathrm { A } = 22 ^ { \circ } , \mathrm { B } = 68 ^ { \circ }$

Accepted Answer

The answer of Solve.
-Angle A and angle B are complementary...

Question 11

Solve.
-The population of a town increased by  80 %  in 5 years. If the population is currently 40,000 , find the population of this town 5 years ago. (Round to the nearest whole, if necessary.)
A) 8000
B) 50,000
C) 32,000
D) 22,222

Accepted Answer

To find the population 5 years ago, let the initial population be P. After a 80% increase, the population becomes P + 0.8P = 1.8P. Given that 1.8P = 40,000, solving for P gives P = 40,000 / 1.8 = 22,222.22, which rounds to 22,222.

Question 12

Solve.
-A car rental agency adverised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 4 days, how many whole miles can you drive if you only have $200 to spens.
A) 50
B) 572
C) 276
D) 21

Accepted Answer

First, calculate the cost for 4 days: 4 days * $29.95/day = $119.80. Subtract this from $200 to find the remaining budget for miles: $200 - $119.80 = $80.20. Divide this by the cost per mile: $80.20 / $0.29/mile = 276.55 miles. Since only whole miles can be driven, the answer is 276 miles.

Question 13

Solve.
-The sum of three consecutive even integers is 318 . Find the integers.
A)  105,106,107 
B)  104,106,108 
C)  106,108,110 
D)  102,104,106

Accepted Answer

The three consecutive even integers can be represented as x, x+2, and x+4. Their sum is 3x + 6 = 318. Solving for x gives x = 104, so the integers are 104, 106, and 108.

Question 14

Solve.
-A 9-ft. board is cut into 2 pieces so that one piece is 5 feet longer than 3 times the shorter piece. If the shorter piece is  x  feet long, find the lengths of both pieces.
A) shorter piece:  1 ft .; longer piece:  8 ft
B) shorter piece:  22 ft ; longer piece:  27 ft .
C) shorter piece:  4.5 ft ; longer piece:  27 ft .
D) shorter piece:  15 ft ; longer piece:  32 ft .

Accepted Answer

The equation representing the situation is x + 3x + 5 = 9. Solving for x gives x = 1 ft for the shorter piece, and substituting x into 3x + 5 gives 8 ft for the longer piece.

Question 15

Solve the equation for the specified variable.
- V=  lwh  for  w 
A) $w = \frac { V l } { h }$
B) $\mathrm { w } = \frac { \mathrm { Vh } } { \mathrm { l } }$
C)  w=Vlh 
D) $w = \frac { V } { l h }$

Accepted Answer

To solve for $w$, you need to isolate $w$ on one side of the equation. Starting with $V = lwh$, divide both sides by $l$ and $h$ to get $w = \frac{V}{lh}$.

Question 16

Solve.
-The cost C to product x number of tennis rackets is C=190 +18x. The tennis rackets are sold wholesale for $23 each, so revenue R =23x. Find how many tennis rackets the manufacturer needs to produce and sell to break even.
A) 43 tennis rackets
B) 33 tennis rackets
C) 19 tennis rackets
D) 38 tennis rackets

Accepted Answer

The answer of Solve.
-The cost C to product x number...

Question 17

Solve the equation for the specified variable.
-$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for h
A) $h = \frac { b } { 2 A }$
B) $h = \frac { A b } { 2 }$
C) $h = \frac { A } { 2 b }$
D) $h = \frac { 2 \mathrm {~A} } { \mathrm {~b} }$

Accepted Answer

To solve for $h$, multiply both sides by 2 to get rid of the fraction, resulting in $2A = bh$, and then divide both sides by $b$ to isolate $h$, giving $h = \frac{2A}{b}$.

Question 18

Solve.
-A diamond ring sold for $2570.40 including tax. If the tax rate where the diamond was purchased is 7.1%, Find the price of the ring befor the tax was added. (Round to the nearest cent, if necessary.)
A) $182.50
B) $2752.90
C) $2400.00
D) $2387.90

Accepted Answer

The total cost of the diamond ring including tax is $2570.40. To find the price before tax, we divide the total cost by 1 plus the tax rate (expressed as a decimal). The tax rate is 7.1%, or 0.071 in decimal form. So, the calculation is $2570.40 / (1 + 0.071) = $2570.40 / 1.071 ≈ $2400.00.

Question 19

Solve.
-Seven times some number added to 8 amounts to  -10  added to the product of 4 and the number.
A) 18
B)  -18 
C)  -6 
D) 6

Accepted Answer

Let the number be x. The equation is 7x + 8 = 4x - 10. Solving for x, we get 3x = -18, so x = -6.

Question 20

Solve.
-A publisher printed 84 million pages in its production process last year. If this represents a  120 %  increase over the number of pages printed the previous year, how many pages were printed the previous year? (Round to the nearest hundredth million, if necessary.)
A) 14,400 million pages
B) 700 million pages
C) 70 million pages
D) 144 million pages

Accepted Answer

The increase is 120% of the previous year's production, meaning the 84 million pages represent 220% of the previous year's production (100% + 120% = 220%). To find the original amount (100%), divide the new production by 2.2 (since 220% corresponds to a factor of 2.2). 84 million / 2.2 = 38.18 million pages, rounding to the nearest hundredth million doesn't apply here as the correct calculation actually results in 38.18 million pages, not 70 million. The correct calculation should be: Let $ x $ be the number of pages printed the previous year. Then, $ x + 1.20x = 84 $ million pages, which simplifies to $ 2.20x = 84 $ million. Solving for $ x $ gives $ x = \frac{84}{2.20} = 38.18 $ million pages. Therefore, the explanation mistakenly provided an incorrect answer and calculation process. The correct process to find the original number of pages printed the previous year involves dividing the total pages printed last year by the total percentage increase represented as a decimal (in this case, 2.2 for 220%).

Quiz 2: Equations, Inequalities, and Problem Solving

Solve. -A region consists of 2565 thousand acres of farm land. If 30 % of this land is privately owned, find how may acres are not privately owned.

Solve the equation for the specified variable. - d=rt for r

Solve. -A Promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per munite for all calls. if joe's phone bill was $62 under this promotional deal, how many minuts of phone calls did he make? Round to the nearest interher, if necessary .

Solve. -Find the measures of the angles of a triangle if the measure of the first angle is four times the measure of the second angle and the third angle is $30 ^ { \circ }$ more than the second angle.

Solve. -In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 81 and the U.S. won more than China who won more than Romania, how many medals did each team win?

Solve the equation for the specified variable. -I= Prt for P

Solve. -The president of a certain University makes three times as much money as one of the department heads. If the total of there salaries is $250,000 , find each worker's salary.

Solve. -The population of a town increased by 80 % in 5 years. If the population is currently 40,000 , find the population of this town 5 years ago. (Round to the nearest whole, if necessary.)

Solve. -A car rental agency adverised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 4 days, how many whole miles can you drive if you only have $200 to spens.

Solve. -The sum of three consecutive even integers is 318 . Find the integers.

Solve. -A 9-ft. board is cut into 2 pieces so that one piece is 5 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Solve the equation for the specified variable. - V= lwh for w

Solve. -The cost C to product x number of tennis rackets is C=190 +18x. The tennis rackets are sold wholesale for $23 each, so revenue R =23x. Find how many tennis rackets the manufacturer needs to produce and sell to break even.

Solve the equation for the specified variable. - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for h

Solve. -A diamond ring sold for $2570.40 including tax. If the tax rate where the diamond was purchased is 7.1%, Find the price of the ring befor the tax was added. (Round to the nearest cent, if necessary.)

Solve. -Seven times some number added to 8 amounts to -10 added to the product of 4 and the number.

Solve. -A publisher printed 84 million pages in its production process last year. If this represents a 120 % increase over the number of pages printed the previous year, how many pages were printed the previous year? (Round to the nearest hundredth million, if necessary.)