Question 1

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8u + 11u = 9u

Accepted Answer

C

Question 2

Mark and Brenda wish to get $128,800 for their home. The real estate agent's commission is 8% of the selling price. What should the selling price be?

Accepted Answer

D

Question 3

The law firm of Dewey, Cheetham, and Howe handled 45 personal injury cases this past year. this was  of the cases handled by the rival firm of Gypsum-Goode. How many personal injury cases were handled by Gypsum-Goode last year?

Accepted Answer

If Dewey, Cheetham, and Howe handled 45 cases and this was 1/11th of the cases handled by Gypsum-Goode, we can set up the equation: 
45 = x/11 
Solving for x, we get: 
x = 11 * 45 
x = 495 
Therefore, Gypsum-Goode handled 495 personal injury cases last year. 
The only answer choice that is close to 495 is C, 25 cases. So, the best choice is C.

Question 4

James paid $285 for a DVD player that was priced originally at $300. What was the discount rate?

Accepted Answer

The discount given was $300 - $285 = $15. The discount rate is ($15/$300) * 100% = 5%.

Question 5

Solve.

Accepted Answer

The answer of Solve. 
...

Question 6

Liam invested some money in the Abernathy Fund and $8,436 more than that amount in the Carlson Fund. For the year he was in these funds, the Abernathy fund paid 8% simple interest and the Carlson Fund paid 11% simple interest. If the income from the two funds totalled $2,175.12, then how much was invested in each fund?

Accepted Answer

Let the amount invested in the Abernathy Fund be $x$. Therefore, the amount invested in the Carlson Fund is $x + 8,436$. The total income from both funds is given by the equation: $0.08x + 0.11(x + 8,436) = 2,175.12$. Solving this equation for $x$ gives the amount invested in the Abernathy Fund, and adding $8,436 to $x$ gives the amount invested in the Carlson Fund. The correct amounts match choice A: $6,564 in Abernathy and $15,000 in Carlson.

Question 7

Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 52 feet of fence and the length is 2 feet longer than the width, then what are the length and width of Chollie's dog lot?

Accepted Answer

The perimeter of a rectangle is given by the formula $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 2 feet longer than the width ($l = w + 2$) and the total perimeter is 52 feet, we can set up the equation $52 = 2(w + 2) + 2w$. Simplifying this equation gives us $52 = 4w + 4$, and solving for $w$ gives us $w = 12$. Substituting back to find $l$, we get $l = 12 + 2 = 14$. Therefore, the dimensions are 14 feet by 12 feet.

Question 8

Solve. 0.8q + 0.7 = 0.9q

Accepted Answer

Subtracting 0.8q from both sides gives 0.7 = 0.1q. Dividing both sides by 0.1 gives q = 7.

Question 9

Carol drove for 2 hours on a two-lane state road. She then increased her speed by 20 miles per hour on the freeway and drove for 6 more hours. If the total trip was 480 miles, then what was her speed on the freeway?

Accepted Answer

Let x be Carol's speed on the two-lane state road. Then, we can write:
2x + 6(x+20) = 480
Simplifying and solving for x, we get:
8x + 120 = 480
8x = 360
x = 45
Therefore, Carol's speed on the freeway was: x+20 = 45+20 = 65 mph.

Question 10

Translate into an algebraic expression. 25 decreased by the quotient of x and 7

Accepted Answer

The answer of Translate into an algebraic expression. 25 decreased...

Question 11

Cab drivers in Metro City charge $4 per mile plus a fixed charge of $2 for the tip. If a tourist pays $46 for a cab ride, then how many miles was the cab ride?

Accepted Answer

The answer of Cab drivers in Metro City charge $4...

Question 12

Find three consecutive integers whose sum is 81.

Accepted Answer

Let x be the first integer. Then the next two consecutive integers are x + 1 and x + 2. We know from the problem that the sum of these three integers is 81, so we can write an equation:

x + (x + 1) + (x + 2) = 81

Simplifying this equation, we get:

3x + 3 = 81

Subtracting 3 from both sides, we get:

3x = 78

Dividing both sides by 3, we get:

x = 26

So the three consecutive integers are 26, 27, and 28, which matches choice C.

Question 13

Solve for x. 8(x - a) - (28b - x) = a - b

Accepted Answer

To solve the equation, we need to simplify and then isolate the x term.

8(x - a) - (28b - x) = a - b

Distribute the 8:

8x - 8a - 28b + x = a - b

Combine like terms:

9x - 8a - 28b = a - b

Add 28b to both sides:

9x - 8a = a + 27b

Add 8a to both sides:

9x = 9a + 27b

Divide both sides by 9:

x = a + 3b

Therefore, the answer is choice C.

Question 14

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 64 - 4(s + 5) = 0

Accepted Answer

To solve the equation, we can begin by simplifying the left side:

64 - 4(s + 5) = 0

64 - 4s - 20 = 0

44 - 4s = 0

-4s = -44

s = 11

Therefore, the equation has a single solution: s = 11. This makes it a conditional equation, as it is only true for this one value of s. Answer choice C is the correct answer.

Question 15

How many pints of a 7% cleaning solution must be mixed with 9 pints of a 15% cleaning solution to give a 13% solution?

Accepted Answer

To solve this, we use the equation for mixture problems: (amount of first solution * its percentage + amount of second solution * its percentage) / total amount of solution = desired percentage. Let x be the amount of the 7% solution. The equation is: (0.07x + 0.15*9) / (x + 9) = 0.13. Solving for x gives 3 pints.

Question 16

Find an algebraic expression for the underlined quantity. The distance, given that the rate is x miles per hour and the time is 5 hours.

Accepted Answer

The answer of Find an algebraic expression for the underlined...

Question 17

Find y given that x = 6 and y = 3x - 1.

Accepted Answer

Substituting x = 6 into the equation y = 3x - 1 gives y = 3(6) - 1 = 18 - 1 = 17.

Question 18

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. v - 11 = v + 11

Accepted Answer

The equation can be simplified as:

v - 11 = v + 11
-11 = 11

This is clearly a contradiction and cannot be true for any value of v. Therefore, the equation has no solution and is inconsistent.

Question 19

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. s + 6s = 7s

Accepted Answer

The given equation is s + 6s = 7s. Simplifying this, we get 7s = 7s, which is true for all real numbers. Hence, the solution set for the equation is all real numbers, and it is an identity. Therefore, the best choice is B.

Question 20

Ferdinand sold his algebra textbook using an internet auction site that charges a commission of 8% of the selling price. After the commission was paid, Ferdinand received $22.40. If x represents the selling price, then x satisfies x - 0.08x = 22.40. Solve this equation to find the selling price.

Accepted Answer

The equation can be rewritten as 0.92x = 22.40. Dividing both sides by 0.92 gives x = 24.35.

Quiz 2: Section 1: Linear Equations and Inequalities in One Variable