Question 1

Solve.
-A number divided by eight is 328. What is the number?

Accepted Answer

To find the number, multiply 328 by 8. The equation is x/8 = 328, so x = 328 * 8 = 2624.

Question 2

Write an algebraic expression for the quantities being compared.
-The first angle of a triangle is double the third angle. The second angle of a triangle is 34 degrees less than the third angle.

Accepted Answer

The first angle is double the third angle, so if the third angle is $x$, the first angle is $2x$. The second angle is 34 degrees less than the third angle, so it is $x - 34$.

Question 3

Solve.
-Two cars start from the same point and travel in the same direction. If one car is traveling 56 miles per hour and the other car is traveling at 45 miles per hour, how far apart will they be after 7.7 hours?

Accepted Answer

The distance between the two cars after 7.7 hours can be found by calculating the difference in the distances each car travels. The first car travels $56 \times 7.7$ miles, and the second car travels $45 \times 7.7$ miles. The difference is $(56 - 45) \times 7.7 = 11 \times 7.7 = 84.7$ miles.

Question 4

Write an algebraic expression for the quantities being compared.
-The attendance on Monday was 43 people more than on Tuesday. The attendance on Wednesday was 44 people fewer than on Tuesday.

Accepted Answer

Let $x$ represent the attendance on Tuesday. The attendance on Monday is 43 more than Tuesday, so it's $x + 43$. The attendance on Wednesday is 44 fewer than Tuesday, so it's $x - 44$.

Question 5

Solve.
-The inventory at AutoPlace is one-eighth the inventory at CarMart. If AutoPlace has 168 vehicles on the lot, how many vehicles does CarMart have in stock?

Accepted Answer

To find the inventory at CarMart, multiply the inventory at AutoPlace by 8 (since AutoPlace has 1/8 the inventory of CarMart). 168 * 8 = 1344 vehicles.

Question 6

Solve.
-Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 7 miles per hour. In how many hours will the two trains be 98.8 miles apart?

Accepted Answer

The answer of Solve.
-Two trains leave a train station at...

Question 7

Solve.
-The force of gravity on a planet varies with the mass of the planet. If the force of gravity on a planet in a distant solar system is about four and one half times that of Earth, how much would an object weighing 270 pounds on
Earth weigh on this planet?

Accepted Answer

To find the weight of the object on the distant planet, multiply the Earth weight by the gravity factor (4.5). So, $270 \text{ lb} \times 4.5 = 1215 \text{ lb}$.

Question 8

Solve.
-What number minus 216 gives 551?

Accepted Answer

To find the number, we add 216 to 551, which equals 767.

Question 9

Solve.
-The cost of renting a scooter is $18 a day plus 5 cents per mile. How far can Michelle drive in one day if she only has $41?

Accepted Answer

Michelle has $41 and the daily rental cost is $18, leaving her with $23 for mileage. At 5 cents per mile, she can drive 460 miles ($23 / $0.05 per mile = 460 miles).

Question 10

Solve.
-A motorcycle shop maintains an inventory of three times as many new bikes as used bikes. If there are 105 new bikes, how many used bikes are now in stock?

Accepted Answer

The shop has three times as many new bikes as used bikes. Given there are 105 new bikes, dividing by 3 gives the number of used bikes: 105 / 3 = 35 used bikes.

Question 11

Solve.
-What number added to 330 gives 729?

Accepted Answer

To find the number added to 330 to get 729, subtract 330 from 729: 729 - 330 = 399.

Question 12

Solve.
-When fifteen is reduced by one-third of a number, the result is 9. Find the number.

Accepted Answer

The equation to solve this problem is 15 - (1/3)x = 9. Solving for x gives x = 18.

Question 13

Solve.
-Seven times a number is five. What is the number?

Accepted Answer

The equation to solve is 7x = 5. Dividing both sides by 7 gives x = 5/7.

Question 14

Write an algebraic expression for the quantities being compared.
-At Dave's Deli, the reuben sandwich cost $1.65 more than the turkey sandwich.

Accepted Answer

The correct expression is $x + 1.65 =$ the cost of the reuben sandwich, where $x$ represents the cost of the turkey sandwich. This indicates that the reuben sandwich costs $1.65 more than the turkey sandwich.

Question 15

Write an algebraic expression for the quantities being compared.
-Evan works 12 hours per week more than Marc.

Accepted Answer

The correct expression is $x + 12$, where $x$ represents the number of hours Marc works, and $x + 12$ represents the number of hours Evan works, indicating Evan works 12 hours more than Marc.

Question 16

Solve.
-Ten less than ten times a number is the same as twelve times the number. Find the number.

Accepted Answer

The answer of Solve.
-Ten less than ten times a number...

Question 17

Solve.
-A promotional deal for phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $70 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest
Integer, if necessary.

Accepted Answer

The answer of Solve.
-A promotional deal for phone service charges...

Question 18

Solve.
-When six is subtracted from one-fourth of a number the result is 36. What is the original number?

Accepted Answer

The answer of Solve.
-When six is subtracted from one-fourth of...

Question 19

Write an algebraic expression for the quantities being compared.
-The length of a rectangle is 28 feet more than double the width.

Accepted Answer

The answer of Write an algebraic expression for the quantities...

Question 20

Solve.
-Larry makes $24 per hour for a 40-hour week and time an a half for every hour over 40 hours. If Larry made $1500 last week, how many overtime hours did he work?

Accepted Answer

The answer of Solve.
-Larry makes $24 per hour for a...

Quiz 2: Equations, Inequalities, and Applications

Solve. -A number divided by eight is 328. What is the number?

Write an algebraic expression for the quantities being compared. -The first angle of a triangle is double the third angle. The second angle of a triangle is 34 degrees less than the third angle.

Solve. -Two cars start from the same point and travel in the same direction. If one car is traveling 56 miles per hour and the other car is traveling at 45 miles per hour, how far apart will they be after 7.7 hours?

Write an algebraic expression for the quantities being compared. -The attendance on Monday was 43 people more than on Tuesday. The attendance on Wednesday was 44 people fewer than on Tuesday.

Solve. -The inventory at AutoPlace is one-eighth the inventory at CarMart. If AutoPlace has 168 vehicles on the lot, how many vehicles does CarMart have in stock?

Solve. -Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 7 miles per hour. In how many hours will the two trains be 98.8 miles apart?

Solve. -The force of gravity on a planet varies with the mass of the planet. If the force of gravity on a planet in a distant solar system is about four and one half times that of Earth, how much would an object weighing 270 pounds on Earth weigh on this planet?

Solve. -What number minus 216 gives 551?

Solve. -The cost of renting a scooter is $18 a day plus 5 cents per mile. How far can Michelle drive in one day if she only has $41?

Solve. -A motorcycle shop maintains an inventory of three times as many new bikes as used bikes. If there are 105 new bikes, how many used bikes are now in stock?

Solve. -What number added to 330 gives 729?

Solve. -When fifteen is reduced by one-third of a number, the result is 9. Find the number.

Solve. -Seven times a number is five. What is the number?

Write an algebraic expression for the quantities being compared. -At Dave's Deli, the reuben sandwich cost $1.65 more than the turkey sandwich.

Write an algebraic expression for the quantities being compared. -Evan works 12 hours per week more than Marc.

Solve. -Ten less than ten times a number is the same as twelve times the number. Find the number.

Solve. -A promotional deal for phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $70 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest Integer, if necessary.

Solve. -When six is subtracted from one-fourth of a number the result is 36. What is the original number?

Write an algebraic expression for the quantities being compared. -The length of a rectangle is 28 feet more than double the width.

Solve. -Larry makes $24 per hour for a 40-hour week and time an a half for every hour over 40 hours. If Larry made $1500 last week, how many overtime hours did he work?