Equations And Inequalities Test! Math Trivia Quiz

1. Write as a variable expression: a number times 11.

X +11

X - 11

11x

11 - x

The correct answer is 11x because the expression "a number times 11" can be represented as 11 multiplied by the variable x.

Explanation

The correct answer is 11x because the expression "a number times 11" can be represented as 11 multiplied by the variable x.

2. Suppose you must maintain a balance of at least $800 in your checking account in order to have free checking. The balance in your account is $849.50 before you write a check for $45. How much cash can you withdraw from the account and still have free checking?

If you must maintain a balance of at least $800 in your checking account to have free checking, and your balance is $849.50 before writing a check for $45, you can withdraw $4.50 and still have free checking. This is because after subtracting $45 from the balance, you will have $804.50 remaining, which is still above the required minimum balance of $800.

Explanation

If you must maintain a balance of at least $800 in your checking account to have free checking, and your balance is $849.50 before writing a check for $45, you can withdraw $4.50 and still have free checking. This is because after subtracting $45 from the balance, you will have $804.50 remaining, which is still above the required minimum balance of $800.

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3. Write as a variable expression: a number of more than 98.

98x

98 - x

98 + x

X - 98

The correct answer is "98 + x" because it represents a number that is greater than 98. The addition of 98 and x implies that x is a positive number, making the sum greater than 98.

Explanation

The correct answer is "98 + x" because it represents a number that is greater than 98. The addition of 98 and x implies that x is a positive number, making the sum greater than 98.

4. Compact disks are on sale for $2 off the regular price. Suppose you buy two CDs and pay a total of $13.98. What is the regular price of each CD?

The regular price of each CD is $8.99. This can be determined by subtracting the $2 discount from the total price of $13.98, which gives us $11.98. Since two CDs were purchased, we can divide $11.98 by 2 to find the regular price of each CD, which is $5.99. However, since the question states that the CDs are on sale for $2 off the regular price, we need to subtract $2 from $5.99 to find the actual regular price, which is $3.99. Therefore, the correct answer is $8.99, $8.99.

Explanation

The regular price of each CD is $8.99. This can be determined by subtracting the $2 discount from the total price of $13.98, which gives us $11.98. Since two CDs were purchased, we can divide $11.98 by 2 to find the regular price of each CD, which is $5.99. However, since the question states that the CDs are on sale for $2 off the regular price, we need to subtract $2 from $5.99 to find the actual regular price, which is $3.99. Therefore, the correct answer is $8.99, $8.99.

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5.

A

B

C

D

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Explanation

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6.

A

B

C

D

not-available-via-ai

Explanation

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7. The cost of renting a car is $23 per day plus $.15 per mile, m, driven. If the car is rented for 2 days, determine the mileage for which the cost of renting the car would be less than $67. (write the verbal answer in the space provided) Use words when expressing inequalities such as "less than" "less than or equal to" "greater than" "greater than or equal to" Example answer: "m is greater than 12"

The cost of renting the car is determined by the formula: cost = 23 + 0.15m, where m represents the mileage driven. To find the mileage for which the cost is less than $67, we set up the inequality: 23 + 0.15m

Explanation

The cost of renting the car is determined by the formula: cost = 23 + 0.15m, where m represents the mileage driven. To find the mileage for which the cost is less than $67, we set up the inequality: 23 + 0.15m

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8. Find three consecutive integers with sum 168. Which is the greatest of the three?

59

57

19

53

To find three consecutive integers with a sum of 168, we can set up the equation x + (x+1) + (x+2) = 168, where x is the first integer. Simplifying this equation, we get 3x + 3 = 168. Solving for x, we find that x = 55. Therefore, the three consecutive integers are 55, 56, and 57. Among these, 57 is the greatest.

Explanation

To find three consecutive integers with a sum of 168, we can set up the equation x + (x+1) + (x+2) = 168, where x is the first integer. Simplifying this equation, we get 3x + 3 = 168. Solving for x, we find that x = 55. Therefore, the three consecutive integers are 55, 56, and 57. Among these, 57 is the greatest.

9. What is the value of m in the equation 2m - (m + 1) = 0?

-1

1

0

.3333333333333333333333333

To find the value of m in the equation 2m - (m + 1) = 0, we can simplify the equation by removing the parentheses. This gives us 2m - m - 1 = 0. Combining like terms, we get m - 1 = 0. To isolate m, we can add 1 to both sides of the equation, resulting in m = 1. Therefore, the value of m in the equation is 1.

Explanation

To find the value of m in the equation 2m - (m + 1) = 0, we can simplify the equation by removing the parentheses. This gives us 2m - m - 1 = 0. Combining like terms, we get m - 1 = 0. To isolate m, we can add 1 to both sides of the equation, resulting in m = 1. Therefore, the value of m in the equation is 1.

10. Shoe sizes and foot length are related by the formula S = 3F - 24, where S represents the shoe size and F represents the length of the foot, in inches. Solve the formula for F.

F = 8S

F = 24S - 3

F = (S + 24) / 3

F = 24S + 3

To solve the formula for F, we need to isolate F on one side of the equation. In the given options, the equation F = (S + 24) / 3 accomplishes this. By dividing both sides of the equation by 3, we can isolate F and solve for it in terms of S. Therefore, the correct answer is F = (S + 24) / 3.

Explanation

To solve the formula for F, we need to isolate F on one side of the equation. In the given options, the equation F = (S + 24) / 3 accomplishes this. By dividing both sides of the equation by 3, we can isolate F and solve for it in terms of S. Therefore, the correct answer is F = (S + 24) / 3.

11. What is the value of w in the equation? 1 w + 7 = 2w - 2 2

6

3.6

3.333333333333333333

2

In the given equation, we have w + 7 = 2w - 2. To find the value of w, we need to isolate the variable on one side of the equation. To do this, we can subtract w from both sides, which gives us 7 = w - 2. Next, we can add 2 to both sides to get w = 9. Therefore, the value of w in the equation is 9.

Explanation

In the given equation, we have w + 7 = 2w - 2. To find the value of w, we need to isolate the variable on one side of the equation. To do this, we can subtract w from both sides, which gives us 7 = w - 2. Next, we can add 2 to both sides to get w = 9. Therefore, the value of w in the equation is 9.

12. In the set of positive integers, what is the solution set of the inequality 4x - 3 < 13?

{0, 1, 2, 3}

{1, 2, 3}

{1, 2, 3, 4}

{4, 5, 6, 7, 8, ...}

The solution set of the inequality 4x - 3

Explanation

The solution set of the inequality 4x - 3

13. Which value of x is in the solution set of the inequality -4x + 2 > 10?

-2

-4

3

2

The correct answer is -4. To find the solution set of the inequality -4x + 2 > 10, we need to isolate the variable x. Subtracting 2 from both sides of the inequality gives -4x > 8. Dividing both sides by -4 (and flipping the inequality sign) gives x

Explanation

The correct answer is -4. To find the solution set of the inequality -4x + 2 > 10, we need to isolate the variable x. Subtracting 2 from both sides of the inequality gives -4x > 8. Dividing both sides by -4 (and flipping the inequality sign) gives x

14. Which of the following solves the equation 8 -(2x - 6) = 22?

-10

0

4

-4

To solve the equation, we need to simplify the expression on the left side. We can start by distributing the negative sign to the terms inside the parentheses. This gives us 8 - 2x + 6 = 22. Next, we can combine like terms by adding 8 and 6, which gives us 14 - 2x = 22. To isolate the variable, we can subtract 14 from both sides of the equation, resulting in -2x = 8. Finally, we can solve for x by dividing both sides by -2, giving us x = -4. Therefore, the correct answer is 4.

Explanation

To solve the equation, we need to simplify the expression on the left side. We can start by distributing the negative sign to the terms inside the parentheses. This gives us 8 - 2x + 6 = 22. Next, we can combine like terms by adding 8 and 6, which gives us 14 - 2x = 22. To isolate the variable, we can subtract 14 from both sides of the equation, resulting in -2x = 8. Finally, we can solve for x by dividing both sides by -2, giving us x = -4. Therefore, the correct answer is 4.

15.

A

B

C

D

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Explanation

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16. If 2m + 2p = 16, p equals

16 + 2m

9m

16 - m

8 - m

The equation given is 2m + 2p = 16. To find the value of p, we need to isolate it on one side of the equation. We can start by subtracting 2m from both sides, which gives us 2p = 16 - 2m. To further isolate p, we divide both sides by 2, resulting in p = (16 - 2m) / 2. Simplifying this expression, we get p = 8 - m. Therefore, the correct answer is 8 - m.

Explanation

The equation given is 2m + 2p = 16. To find the value of p, we need to isolate it on one side of the equation. We can start by subtracting 2m from both sides, which gives us 2p = 16 - 2m. To further isolate p, we divide both sides by 2, resulting in p = (16 - 2m) / 2. Simplifying this expression, we get p = 8 - m. Therefore, the correct answer is 8 - m.

17.

20 and 30

30 and 40

25 and 35

20 and 40

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Explanation

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18. A prom ticket at Smith High School is $120. Tom is going to save money for the ticket by walking his neighbor’s dog for $15 per week, w. If Tom already has saved $22, what is the minimum number of weeks Tom must walk the dog to earn enough to pay for the prom ticket?

(write the verbal answer in the space provided)

Use one of the following words when expressing the inequality "less than" "less than or equal to" "greater than" "greater than or equal to"

Example answer: "w is greater than 12"

Tom needs to save $120 - $22 = $98 for the prom ticket. He earns $15 per week by walking his neighbor's dog. To earn $98, he needs to work for at least $98 / $15 = 6.53 weeks. Since Tom cannot work for a fraction of a week, he needs to work for at least 7 weeks to earn enough money for the prom ticket. Therefore, the minimum number of weeks Tom must walk the dog is greater than or equal to 7.

Explanation

Tom needs to save $120 - $22 = $98 for the prom ticket. He earns $15 per week by walking his neighbor's dog. To earn $98, he needs to work for at least $98 / $15 = 6.53 weeks. Since Tom cannot work for a fraction of a week, he needs to work for at least 7 weeks to earn enough money for the prom ticket. Therefore, the minimum number of weeks Tom must walk the dog is greater than or equal to 7.

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