Question 1

Solve the problem.
-Brand $X$ copier advertises that its copiers run $10 \%$ longer between service calls than its competitor. If Brand X copiers run 42,400 copies between service calls, how many copies would the competitor run (to the nearest copy)?
A) 38,160 copies
B) 46,640 copies
C) 22,316 copies
D) 38,545 copies

Accepted Answer

The answer of Solve the problem.
-Brand $X$ copier advertises that...

Question 2

Solve the problem.
-A high school graduating class is made up of 394 students. There are 74 more girls than boys. How many boys are in the class?
A) 160 boys
B) 394 boys
C) 74 boys
D) 234 boys

Accepted Answer

The total number of students is 394, and there are 74 more girls than boys. Let the number of boys be x. Then, the number of girls is x + 74. The equation to represent the total number of students is x + (x + 74) = 394. Solving for x gives x = 160, which represents the number of boys.

Question 3

Solve the problem.
-A baseball team played 163 complete games last season. They had 53 fewer wins than losses. How many games did the team win?
A) 163 games
B) 55 games
C) 108 games
D) 53 games

Accepted Answer

The team played 163 games in total. Let's denote the number of wins as W and the number of losses as L. We are given that the team had 53 fewer wins than losses, which can be represented as W = L - 53. Since the total number of games is the sum of wins and losses (W + L = 163), we can substitute the first equation into the second to solve for L: (L - 53) + L = 163. Simplifying, we get 2L = 216, so L = 108. Substituting L back into the equation W = L - 53 gives us W = 108 - 53 = 55. Therefore, the team won 55 games.

Question 4

Solve the problem.
-Every basketball season Bill competes in a free throw contest. This year Bill was successful at 0.6 of his free throws. If he succeeded at 18 free throws, how many free throws did he attempt?
A) 1800.6 free throws
B) 108 free throws
C) 30 free throws
D) 10.8 free throws

Accepted Answer

Bill's success rate was 0.6, meaning he made 60% of his attempts. To find the total attempts, divide the number of successful shots (18) by the success rate (0.6): 18 / 0.6 = 30.

Question 5

Solve the problem.
-CopyMart charges $\$ 22$ plus $40 \$$ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $\$ 62.40$ ? (Hint: $40 \$=\$ 0.40$ )
A) 111 brochures
B) 12 brochures
C) 42 brochures
D) 101 brochures

Accepted Answer

The answer of Solve the problem.
-CopyMart charges $\$ 22$ plus...

Question 6

Solve the problem.
-Recently, the cost of 196 -oz jars of baby food was $\$ 11.78$. What was the cost of one jar?
A) $\$ 1.86$
B) $\$ 0.62$
C) $\$ 0.31$
D) $\$ 1.24$

Accepted Answer

The cost of one jar is found by dividing the total cost by the number of jars. \$11.78 / 6 = \$1.963, rounding to the nearest cent gives \$1.96, which is not an option provided. The correct calculation should be \$11.78 / 19 = \$0.62, assuming a typo in the number of jars (196 should be 19). However, without the correct context or options matching the calculation, it's challenging to provide a precise answer. The closest option based on the given calculation is B) \$0.62.

Question 7

Solve.
-The height of the tallest building in Anne's home town is 719 feet, which is about 350 feet taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?
A) $482 \mathrm{ft}$
B) $350 \mathrm{ft}$
C) $1069 \mathrm{ft}$
D) $369 \mathrm{ft}$

Accepted Answer

The answer of Solve.
-The height of the tallest building in...

Question 8

Solve.
-The area of Mark's backyard is about 5 times the area of Jon's backyard. The area of Mark's backyard is $3590 \mathrm{ft}^{2}$. What is the area of Jon's backyard?
A) $3590 \mathrm{ft}^{2}$
B) $3585 \mathrm{ft}^{2}$
C) $831 \mathrm{ft}^{2}$
D) $718 \mathrm{ft}^{2}$

Accepted Answer

The area of Jon's backyard is $ \frac{3590}{5} = 718 \mathrm{ft}^{2} $.

Question 9

Solve.
-A city government budgeted $\$ 39.7$ million for public transportation. This was $\$ 16.4$ million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?
A) $\$ 22.8$ million
B) $\$ 24.3$ million
C) $\$ 23.3$ million
D) $\$ 27.3$ million

Accepted Answer

To find the amount budgeted for parks and recreation, subtract the additional amount from the public transportation budget: $ \$39.7 \text{ million} - \$16.4 \text{ million} = \$23.3 \text{ million} $.

Question 10

Solve.
-Elaine was cooking dinner for some friends. She went out to do the shopping and spent $\$ 60$. She spent twice as much on food as on drinks. How much did she spend on each?
A) Drinks: $\$ 15$; food: $\$ 45$
B) Drinks: $\$ 30$; food: $\$ 60$
C) Drinks: $\$ 20$; food: $\$ 40$
D) Drinks: $\$ 15$; food: $\$ 30$

Accepted Answer

Elaine spent twice as much on food as on drinks. Let the amount spent on drinks be $ x $. Then, the amount spent on food is $ 2x $. The total spent is $ x + 2x = 3x = 60 $. Solving for $ x $, we get $ x = 20 $. Therefore, she spent $\$ 20$ on drinks and $\$ 40$ on food.

Question 11

Solve.
-A 396 -foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is each piece of rope?
A) First: $66 \mathrm{ft}$; second: $132 \mathrm{ft}$; third: $396 \mathrm{ft}$
B) First: $44 \mathrm{ft}$; second: $88 \mathrm{ft}$; third: $264 \mathrm{ft}$
C) First: $50 \mathrm{ft}$; second: $99 \mathrm{ft}$; third: $297 \mathrm{ft}$
D) First: $50 \mathrm{ft}$; second: $99 \mathrm{ft}$; third: $248 \mathrm{ft}$

Accepted Answer

Let the length of the first piece be $x$. The second piece is $2x$ and the third piece is $3 \times 2x = 6x$. The total length is $x + 2x + 6x = 9x = 396$. Solving for $x$ gives $x = 44$, making the lengths $44 \mathrm{ft}$, $88 \mathrm{ft}$, and $264 \mathrm{ft}$ respectively.

Question 12

Solve.
-A car rental business rents a compact car at a daily rate of $\$ 25.20$ plus $20 \$$ per mile. Mike can afford to spend $\$ 57$ on the car rental for one day. How many miles can he drive and stay within his budget? (Hint: $20 \$=\$ 0.20$ )
A) $159 \mathrm{mi}$
B) $154 \mathrm{mi}$
C) $164 \mathrm{mi}$
D) $149 \mathrm{mi}$

Accepted Answer

The total cost of renting the car for one day is $25.20 + 0.20m$, where $m$ is the number of miles driven. Since Mike can afford to spend $57$ dollars, we have the equation:$$25.20 + 0.20m = 57$$Solving for $m$, we get:$$0.20m = 31.80$$$$m = 159$$Therefore, Mike can drive $159$ miles and stay within his budget.

Question 13

Solve.
-You are traveling to your aunt's house that is 207 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?
A) $34.5 \mathrm{mi}$
B) $69 \mathrm{mi}$
C) $103.5 \mathrm{mi}$
D) $138 \mathrm{mi}$

Accepted Answer

The answer of Solve.
-You are traveling to your aunt's house...

Question 14

Solve.
-Greg sold his used electric saw and accessories for $\$ 580$. If he received nine times as much money for the electric saw as he did for the accessories, how much did he receive for the electric saw?
A) $\$ 58$
B) $\$ 522$
C) $\$ 68$
D) $\$ 5220$

Accepted Answer

Let the amount received for the accessories be $x$. Therefore, the amount received for the electric saw is $9x$. The total amount received is $x + 9x = 10x = \$580$. Solving for $x$ gives $x = \$58$, so the electric saw sold for $9x = 9 \times \$58 = \$522$.

Question 15

Solve.
-In West Arlington, taxis charge $\$ 4.50$ plus $50 \$$ per mile for an airport pickup. How far from the airport can Amy travel for $\$ 23.50$ ? (Hint: $50 \$=\$ 0.50$ )
A) $94 \mathrm{mi}$
B) $38 \mathrm{mi}$
C) $47 \mathrm{mi}$
D) $11.75 \mathrm{mi}$

Accepted Answer

The answer of Solve.
-In West Arlington, taxis charge $\$ 4.50$...

Question 16

Solve.
-Bill needs an average of 85 on four tests in science to make the honor roll. What is the lowest score he can receive on the fourth test if his first three scores are 78, 80, and 94?
A) 84
B) 85
C) 88
D) 84.3

Accepted Answer

To achieve an average of 85 over four tests, the total points must be 4 * 85 = 340. The sum of the first three scores is 78 + 80 + 94 = 252. Therefore, the lowest score Bill can receive on the fourth test to reach a total of 340 points is 340 - 252 = 88.

Question 17

Determine whether the given number is a solution of the inequality.
-$x>-12,-7.34$

Accepted Answer

Since $-7.34$ is greater than $-12$, it satisfies the inequality $x > -12$.

Question 18

Determine whether the given number is a solution of the inequality.
-$x>5,1.2$

Accepted Answer

The number $1.2$ is not a solution to the inequality $x > 5$ because $1.2$ is less than $5$.

Question 19

Determine whether the given number is a solution of the inequality.
-$x<3,-3.24$

Accepted Answer

Since $-3.24 < 3$, it satisfies the inequality $x < 3$.

Question 20

Determine whether the given number is a solution of the inequality.
-$x>2,-3.4$

Accepted Answer

The given number $-3.4$ is not a solution of the inequality $x > 2$ because $-3.4$ is less than $2$, not greater.

Quiz 8: Solving Equations and Inequalities

Solve the problem. -Brand $X$ copier advertises that its copiers run $10 \%$ longer between service calls than its competitor. If Brand X copiers run 42,400 copies between service calls, how many copies would the competitor run (to the nearest copy) ?

Solve the problem. -A high school graduating class is made up of 394 students. There are 74 more girls than boys. How many boys are in the class?

Solve the problem. -A baseball team played 163 complete games last season. They had 53 fewer wins than losses. How many games did the team win?

Solve the problem. -Every basketball season Bill competes in a free throw contest. This year Bill was successful at 0.6 of his free throws. If he succeeded at 18 free throws, how many free throws did he attempt?

Solve the problem. -CopyMart charges $\$ 22$ plus $40 \$$ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $\$ 62.40$ ? (Hint: $40 \$=\$ 0.40$ )

Solve the problem. -Recently, the cost of 196 -oz jars of baby food was $\$ 11.78$ . What was the cost of one jar?

Solve. -The height of the tallest building in Anne's home town is 719 feet, which is about 350 feet taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Solve. -The area of Mark's backyard is about 5 times the area of Jon's backyard. The area of Mark's backyard is $3590 \mathrm{ft}^{2}$ . What is the area of Jon's backyard?

Solve. -A city government budgeted $\$ 39.7$ million for public transportation. This was $\$ 16.4$ million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?

Solve. -Elaine was cooking dinner for some friends. She went out to do the shopping and spent $\$ 60$ . She spent twice as much on food as on drinks. How much did she spend on each?

Solve. -A 396 -foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is each piece of rope?

Solve. -A car rental business rents a compact car at a daily rate of $\$ 25.20$ plus $20 \$$ per mile. Mike can afford to spend $\$ 57$ on the car rental for one day. How many miles can he drive and stay within his budget? (Hint: $20 \$=\$ 0.20$ )

Solve. -You are traveling to your aunt's house that is 207 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?

Solve. -Greg sold his used electric saw and accessories for $\$ 580$ . If he received nine times as much money for the electric saw as he did for the accessories, how much did he receive for the electric saw?

Solve. -In West Arlington, taxis charge $\$ 4.50$ plus $50 \$$ per mile for an airport pickup. How far from the airport can Amy travel for $\$ 23.50$ ? (Hint: $50 \$=\$ 0.50$ )

Solve. -Bill needs an average of 85 on four tests in science to make the honor roll. What is the lowest score he can receive on the fourth test if his first three scores are 78, 80, and 94?

Determine whether the given number is a solution of the inequality. - $x>-12,-7.34$

Determine whether the given number is a solution of the inequality. - $x>5,1.2$

Determine whether the given number is a solution of the inequality. - $x<3,-3.24$

Determine whether the given number is a solution of the inequality. - $x>2,-3.4$

Quiz 8: Solving Equations and Inequalities

Solve the problem. -Brand XXX copier advertises that its copiers run 10%10 \%10% longer between service calls than its competitor. If Brand X copiers run 42,400 copies between service calls, how many copies would the competitor run (to the nearest copy) ?

Solve the problem. -A high school graduating class is made up of 394 students. There are 74 more girls than boys. How many boys are in the class?

Solve the problem. -A baseball team played 163 complete games last season. They had 53 fewer wins than losses. How many games did the team win?

Solve the problem. -Every basketball season Bill competes in a free throw contest. This year Bill was successful at 0.6 of his free throws. If he succeeded at 18 free throws, how many free throws did he attempt?

Solve the problem. -CopyMart charges $22\$ 22$22 plus 40$40 \$40$ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $62.40\$ 62.40$62.40 ? (Hint: 40$=$0.4040 \$=\$ 0.4040$=$0.40 )

Solve the problem. -Recently, the cost of 196 -oz jars of baby food was $11.78\$ 11.78$11.78 . What was the cost of one jar?

Solve. -The height of the tallest building in Anne's home town is 719 feet, which is about 350 feet taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Solve. -The area of Mark's backyard is about 5 times the area of Jon's backyard. The area of Mark's backyard is 3590ft23590 \mathrm{ft}^{2}3590ft2 . What is the area of Jon's backyard?

Solve. -A city government budgeted $39.7\$ 39.7$39.7 million for public transportation. This was $16.4\$ 16.4$16.4 million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?

Solve. -Elaine was cooking dinner for some friends. She went out to do the shopping and spent $60\$ 60$60 . She spent twice as much on food as on drinks. How much did she spend on each?

Solve. -A 396 -foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is each piece of rope?

Solve. -A car rental business rents a compact car at a daily rate of $25.20\$ 25.20$25.20 plus 20$20 \$20$ per mile. Mike can afford to spend $57\$ 57$57 on the car rental for one day. How many miles can he drive and stay within his budget? (Hint: 20$=$0.2020 \$=\$ 0.2020$=$0.20 )