Question 1

Suppose that a triangular lot is enclosed with 64 yards of fencing (see the picture). The longest side of the lot is 6 yards longer than 5 times the length of the shortest side. The other side is 23 yards longer than the shortest side. Find the lengths of the three sides of the lot. 
A) 5 yards, 31 yards and 38 yards
B) 5 yards, 31 yards and 28 yards
C) 15 yards, 31 yards and 38 yards
D) 5 yards, 41 yards and 28 yards

Accepted Answer

The answer of Suppose that a triangular lot is enclosed...

Question 2

The plans for an apartment complex provided for 440 apartments, with each apartment having one, two, or three bedrooms. There were to be 30 more three-bedroom than one-bedroom apartments, and the number of two-bedroom apartments was to be 10 less than 3 times the number of one-bedroom apartments. How many apartments of each type were in the plans?
A) 84 one-bedrooms, 242 two-bedrooms, and 117 three-bedrooms
B) 84 one-bedrooms, 245 two-bedrooms, and 113 three-bedrooms
C) 84 one-bedrooms, 242 two-bedrooms, and 114 three-bedrooms
D) 114 one-bedrooms, 252 two-bedrooms, and 114 three-bedrooms
E) 114 one-bedrooms, 242 two-bedrooms, and 144 three-bedrooms

Accepted Answer

Let's represent the number of one-bedroom apartments as x.

According to the problem:
- The number of three-bedroom apartments is 30 more than the number of one-bedroom apartments. So, the number of three-bedroom apartments is x+30.
- The number of two-bedroom apartments is 10 less than 3 times the number of one-bedroom apartments. So, the number of two-bedroom apartments is 3x-10.

We know that the total number of apartments is 440. So:

x + (x+30) + (3x-10) = 440
5x + 20 = 440
5x = 420
x = 84

So, there are 84 one-bedroom apartments in the plans.

Using the values we found before, we can find the number of two-bedroom and three-bedroom apartments:

Number of two-bedroom apartments = 3x-10 = 3(84)-10 = 242
Number of three-bedroom apartments = x+30 = 84+30 = 114

Therefore, there are 84 one-bedrooms, 242 two-bedrooms, and 114 three-bedrooms in the plans. The correct answer choice is C.

Question 3

One of two supplementary angles is 35 times as large as the other. Find the measure of each angle. Please enter your answer as two numbers, listed from least to greatest, separated by a comma.

Accepted Answer

The answer of One of two supplementary angles is 35...

Question 4

The textbook for a biology class cost $17 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book. $__________

Accepted Answer

The answer of The textbook for a biology class cost...

Question 5

At a local restaurant, $245 in tips is to be shared between the server, bartender, and busboy. The server gets $20 more than three times the amount the busboy receives. The bartender gets $50 more than the amount the busboy receives. How much will the server receive? $__________

Accepted Answer

The answer of At a local restaurant, $245 in tips...

Question 6

Solve the equation. $7 n - 5 = 7 n - 4$

Accepted Answer

The answer of Solve the equation. \(7 n - 5...

Question 7

Solve the equation. $6 + 5 t + 3 t = 2 t + 4 t + 8$

Accepted Answer

The answer of Solve the equation. \(6 + 5 t...

Question 8

Solve the equation. $8 y - 6 = 5 y - 9$

Accepted Answer

The answer of Solve the equation. \(8 y - 6...

Question 9

Solve the equation. $9 p + 2 + 3 p = 5 p + 6 p - 5$

Accepted Answer

The answer of Solve the equation. \(9 p + 2...

Question 10

Solve the equation. $9 z - 36 + 12 z - 12 z + 18 = 54$

Accepted Answer

The answer of Solve the equation. \(9 z - 36...

Question 11

At a local restaurant, $315 in tips is to be shared between the server, bartender, and busboy. The server gets $30 more than three times the amount the busboy receives. The bartender gets $60 more than the amount the busboy receives. How much will the server receive?
A) $135
B) $45
C) $165
D) $195
E) $105

Accepted Answer

Let the amount the busboy receives be x. Then, the server receives 3x + 30, and the bartender receives x + 60. The total is x + (3x + 30) + (x + 60) = 315. Simplifying, 5x + 90 = 315, so 5x = 225, and x = 45. The server receives 3(45) + 30 = 165.

Question 12

3 more than 3 times a certain number is the same as 6 less than 2 times the number. Find the number.

Accepted Answer

The answer of 3 more than 3 times a certain...

Question 13

Solve the equation. $3 y - 3 + 6 y - 8 y + 2 = 5$

Accepted Answer

The answer of Solve the equation. \(3 y - 3...

Question 14

Suppose that Michael is paid two times his normal hourly rate for each hour he works over 46 hours in a week. Last week he earned $560 for 51 hours of work. What is his hourly wage? $__________

Accepted Answer

The answer of Suppose that Michael is paid two times...

Question 15

A set of wheels sold in an online auction for $550. This was $40 more than three times the opening bid. How much was the opening bid? $__________

Accepted Answer

The answer of A set of wheels sold in an...

Question 16

The sum of a number plus 10 times the number is 44. What is the number?

Accepted Answer

The answer of The sum of a number plus 10...

Question 17

Solve the equation. $7 p - 2 - 9 p = - 16$

Accepted Answer

The answer of Solve the equation. \(7 p - 2...

Question 18

Solve the equation. $2 p + 18 + 7 p = 63$

Accepted Answer

The answer of Solve the equation. \(2 p + 18...

Question 19

The textbook for a biology class cost $14 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book.
A) $76
B) $85
C) $62
D) $90
E) $104

Accepted Answer

Let x be the cost of the used college algebra textbook.

Then the cost of the biology textbook is 2x + $14.

We know that the sum of the costs of the two books is $128:

x + (2x + $14) = $128

Simplifying this equation, we get:

3x + $14 = $128

Subtracting $14 from both sides, we get:

3x = $114

Dividing both sides by 3, we get:

x = $38

So the cost of the biology textbook is 2x + $14 = $90.

Therefore, the answer is D.

Question 20

A set of wheels sold in an online auction for $560. This was $35 more than three times the opening bid. How much was the opening bid?
A) $175
B) $165
C) $185
D) $180
E) $170

Accepted Answer

The correct equation to solve this problem is $560 = 3x + $35, where x is the opening bid. Solving for x gives $525 = 3x, so x = $175.

Quiz 3: Equations, Inequalities and Problem Solving

Suppose that a triangular lot is enclosed with 64 yards of fencing (see the picture) . The longest side of the lot is 6 yards longer than 5 times the length of the shortest side. The other side is 23 yards longer than the shortest side. Find the lengths of the three sides of the lot.

One of two supplementary angles is 35 times as large as the other. Find the measure of each angle. Please enter your answer as two numbers, listed from least to greatest, separated by a comma.

The textbook for a biology class cost $17 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book. $__________

At a local restaurant, $245 in tips is to be shared between the server, bartender, and busboy. The server gets $20 more than three times the amount the busboy receives. The bartender gets $50 more than the amount the busboy receives. How much will the server receive? $__________

Solve the equation. $7 n - 5 = 7 n - 4$

Solve the equation. $6 + 5 t + 3 t = 2 t + 4 t + 8$

Solve the equation. $8 y - 6 = 5 y - 9$

Solve the equation. $9 p + 2 + 3 p = 5 p + 6 p - 5$

Solve the equation. $9 z - 36 + 12 z - 12 z + 18 = 54$

At a local restaurant, $315 in tips is to be shared between the server, bartender, and busboy. The server gets $30 more than three times the amount the busboy receives. The bartender gets $60 more than the amount the busboy receives. How much will the server receive?

3 more than 3 times a certain number is the same as 6 less than 2 times the number. Find the number.

Solve the equation. $3 y - 3 + 6 y - 8 y + 2 = 5$

Suppose that Michael is paid two times his normal hourly rate for each hour he works over 46 hours in a week. Last week he earned $560 for 51 hours of work. What is his hourly wage? $__________

A set of wheels sold in an online auction for $550. This was $40 more than three times the opening bid. How much was the opening bid? $__________

The sum of a number plus 10 times the number is 44. What is the number?

Solve the equation. $7 p - 2 - 9 p = - 16$

Solve the equation. $2 p + 18 + 7 p = 63$

The textbook for a biology class cost $14 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book.

A set of wheels sold in an online auction for $560. This was $35 more than three times the opening bid. How much was the opening bid?

Quiz 3: Equations, Inequalities and Problem Solving

Suppose that a triangular lot is enclosed with 64 yards of fencing (see the picture) . The longest side of the lot is 6 yards longer than 5 times the length of the shortest side. The other side is 23 yards longer than the shortest side. Find the lengths of the three sides of the lot.

One of two supplementary angles is 35 times as large as the other. Find the measure of each angle. Please enter your answer as two numbers, listed from least to greatest, separated by a comma.

The textbook for a biology class cost $17 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book. $__________

At a local restaurant, $245 in tips is to be shared between the server, bartender, and busboy. The server gets $20 more than three times the amount the busboy receives. The bartender gets $50 more than the amount the busboy receives. How much will the server receive? $__________

Solve the equation. 7n−5=7n−47 n - 5 = 7 n - 47n−5=7n−4

Solve the equation. 6+5t+3t=2t+4t+86 + 5 t + 3 t = 2 t + 4 t + 86+5t+3t=2t+4t+8

Solve the equation. 8y−6=5y−98 y - 6 = 5 y - 98y−6=5y−9

Solve the equation. 9p+2+3p=5p+6p−59 p + 2 + 3 p = 5 p + 6 p - 59p+2+3p=5p+6p−5

Solve the equation. 9z−36+12z−12z+18=549 z - 36 + 12 z - 12 z + 18 = 549z−36+12z−12z+18=54

At a local restaurant, $315 in tips is to be shared between the server, bartender, and busboy. The server gets $30 more than three times the amount the busboy receives. The bartender gets $60 more than the amount the busboy receives. How much will the server receive?

3 more than 3 times a certain number is the same as 6 less than 2 times the number. Find the number.

Solve the equation. 3y−3+6y−8y+2=53 y - 3 + 6 y - 8 y + 2 = 53y−3+6y−8y+2=5

Suppose that Michael is paid two times his normal hourly rate for each hour he works over 46 hours in a week. Last week he earned $560 for 51 hours of work. What is his hourly wage? $__________

A set of wheels sold in an online auction for $550. This was $40 more than three times the opening bid. How much was the opening bid? $__________

The sum of a number plus 10 times the number is 44. What is the number?

Solve the equation. 7p−2−9p=−167 p - 2 - 9 p = - 167p−2−9p=−16

Solve the equation. 2p+18+7p=632 p + 18 + 7 p = 632p+18+7p=63

The textbook for a biology class cost $14 more than twice the cost of a used textbook for college algebra. If the cost of the two books together is $128, find the cost of the biology book.

A set of wheels sold in an online auction for $560. This was $35 more than three times the opening bid. How much was the opening bid?

Solve the equation. $7 n - 5 = 7 n - 4$

Solve the equation. $6 + 5 t + 3 t = 2 t + 4 t + 8$

Solve the equation. $8 y - 6 = 5 y - 9$

Solve the equation. $9 p + 2 + 3 p = 5 p + 6 p - 5$

Solve the equation. $9 z - 36 + 12 z - 12 z + 18 = 54$

Solve the equation. $3 y - 3 + 6 y - 8 y + 2 = 5$

Solve the equation. $7 p - 2 - 9 p = - 16$

Solve the equation. $2 p + 18 + 7 p = 63$