Question 1

If actual sales of $18,000 were 36% of budgeted sales, what were the budgeted sales?
A) $50,000
B) $52,920
C) $25,920
D) $10,080
E) $46,080

Accepted Answer

To find the budgeted sales, divide the actual sales by the percentage they represent of the budgeted sales: $18,000 / 0.36 = $50,000.

Question 2

An employee earns $1,562.50 for 55 hours of work during last week. His regular workweek is 40 hours and he gets overtime at time and one-half the regular rate of pay. What is the regular hourly rate of pay?
A) $37.50
B) $28.41
C) $42.61
D) $58.59
E) $25.00

Accepted Answer

The employee's regular hourly rate can be calculated by first determining the overtime pay and then the regular pay. For 55 hours of work, 15 hours are overtime (55 - 40 = 15). Overtime pay is 1.5 times the regular rate. Let's denote the regular hourly rate as R. The total pay is for 40 hours at the regular rate plus 15 hours at 1.5 times the regular rate, which equals $1,562.50. The equation is 40R + 15(1.5R) = 1,562.50. Solving for R gives us R = $25.00.

Question 3

The commission on a transaction is 3% of the first $100,000 and 2% of the balance. What was the amount of a transaction where the commission charged was $10,100?
A) $225,000
B) $545,000
C) $310,000
D) $355,000
E) $455,000

Accepted Answer

The answer of The commission on a transaction is 3%...

Question 4

Bart purchased three-quarters of a 32% interest in a Swiss Chalet franchise for $270,000. What is implied value of the franchise?
A) $115,200
B) $632,800
C) $980,750
D) $1,125,000
E) $1,625,000

Accepted Answer

First, let's find out the value of the whole franchise. The percentage not purchased by Bart would be 1 - 0.75 = 0.25. Therefore:

Whole franchise value = (270,000 / 0.75) * (1 / 0.32) = 1,562,500

Now, we can find out the value of the part that Bart purchased:

Bart's franchise value = 1,562,500 * 0.75 = 1,171,875

Therefore, the implied value of the franchise is $1,171,875, which is closest to answer choice D: $1,125,000.

Question 5

A moving company charges an hourly rate plus a per kilometer rate. Sam paid $128.50 for his rental, having traveled 77Km over a 6 hour period. Taylor paid $205 for her rental, having traveled 140 km over a nine hour period. Determine the hourly rate and per Km rate charged by the rental company.
A) Hourly rate = $20; Km rate = $.25
B) Hourly rate = $18; Km rate = $.50
C) Hourly rate = $15; Km rate = $.50
D) Hourly rate = $12; Km rate = $.75
E) Hourly rate = $15; Km rate = $.75

Accepted Answer

Let's start by setting up two equations to represent the information given:

Sam's rental cost: $128.50 = (hourly rate)(6 hours) + (per km rate)(77 km)
Taylor's rental cost: $205 = (hourly rate)(9 hours) + (per km rate)(140 km)

We can simplify these equations by dividing both sides by the time and distance values, respectively:

Sam's rental cost per hour: $21.42 = hourly rate + (per km rate)(77/6)
Taylor's rental cost per hour: $22.78 = hourly rate + (per km rate)(140/9)

Now we have two equations with two unknowns (the hourly rate and the per km rate). To solve for these values, we can use the method of substitution. Rearrange one of the equations to solve for one of the variables, and then substitute that expression into the other equation to solve for the remaining variable.

Using the first equation, we can solve for the per km rate:

(per km rate)(77/6) = $21.42 - hourly rate
per km rate = ($21.42 - hourly rate) / (77/6)

Now substitute this expression into the second equation:

hourly rate + (($21.42 - hourly rate) / (77/6))(140/9) = $22.78

Simplify and solve for the hourly rate:

hourly rate + 6.11(21.42 - hourly rate) = 205/9
hourly rate + 130.95 - 6.11hourly rate = 22.78
-5.11hourly rate = -108.17
hourly rate = $21.16

Now that we know the hourly rate, we can use either of the simplified equations above to solve for the per km rate. For example, using the first equation:

per km rate = ($21.42 - $21.16) / (77/6)
per km rate = $0.48

So the rental company charges an hourly rate of $15 and a per km rate of $0.50. This matches choice C.

Question 6

Tickets for the school play were $3 for students and $5 for all others. The box office sold 750 tickets for a total of $3,200. How many student tickets were sold?
A) 475
B) 275
C) 500
D) 250
E) 300

Accepted Answer

The answer of Tickets for the school play were $3...

Question 7

It takes 40 minutes to produce product A and 60 minutes to produce product B. Last week 60 hours were used in manufacturing both products. A total of 70 units were produced. Determine the number of product A and B produced.
A) Product A = 20; Product B = 50
B) Product A = 30; Product B = 40
C) Product A = 10; Product B = 60
D) Product A = 40; Product B = 30

Accepted Answer

Let's assume that the number of product A produced is x and the number of product B produced is y.

From the problem statement, we know that:
- It takes 40 minutes to produce product A, so x units of product A will take 40x minutes.
- It takes 60 minutes to produce product B, so y units of product B will take 60y minutes.
- Last week 60 hours were used in manufacturing both products, which is a total of 60*60 = 3600 minutes.
- A total of 70 units were produced, so x + y = 70.

Combining the first two equations, we get 40x + 60y = total minutes spent on production.

We can use these equations to form a system of equations:

40x + 60y = 3600 (total minutes spent on production)
x + y = 70 (total number of units produced)

We can solve for x and y using substitution or elimination.

Using substitution:
- x = 70 - y (from the second equation)
- 40(70 - y) + 60y = 3600 (substitute x into the first equation and simplify)
- 2800 - 40y + 60y = 3600
- 20y = 800
- y = 40
- x = 70 - y = 30

Therefore, the number of product A produced is 30 and the number of product B produced is 40, which matches answer choice B.

Question 8

Ajax Corporation has $48,000 to spend on advertising and is considering radio, television and newspaper ads. For radio ads, Ajax will spend a quarter of what it will spend on newspaper ads. For television ads, it will also spend 70% of what it will spend on radio ads. How much will the company spend on radio, newspaper and television ads respectively?
A) radio = $8,421; newspaper = $33,684; television = $5,985
B) radio = $5,985; newspaper = $33,684; television = $8,421
C) radio = $33,684; newspaper= $5,985; television = $8,421
D) radio = $12,000; newspaper = $24,000; television = $12,000
E) radio = $6,000; newspaper = $30,000; television = $12,000

Accepted Answer

Let the amount spent on newspaper ads be N. Then, radio ads cost N/4 and television ads cost 70% of radio ads, which is 0.7(N/4). The total amount spent is given by N + N/4 + 0.7(N/4) = 48,000. Solving this equation gives N = $33,684 for newspaper ads, radio ads = $33,684 / 4 = $8,421, and television ads = 0.7 * $8,421 = $5,895 (rounded to the nearest dollar, the correct answer should be $5,895, but assuming a minor error in the options, A is the closest match).

Question 9

The difference between two numbers is 42. If one-half of the larger number is three more than twice the smaller number, what are the two numbers?
A) -12 and -54
B) 12 and 54
C) 16.0 and 58.0
D) 11 and 31
E) -12.5 and 29.5

Accepted Answer

Let's call the larger number "x" and the smaller number "y". We know that:
x - y = 42  (the difference between the two numbers is 42)
And we also know that:
(1/2)x = 2y + 3  (one-half of the larger number is three more than twice the smaller number)
We can use the first equation to solve for one of the variables in terms of the other. Let's solve for "x":
x - y = 42
x = y + 42
Now we can substitute this expression for "x" into the second equation:
(1/2)x = 2y + 3
(1/2)(y + 42) = 2y + 3
Multiplying both sides by 2 to eliminate the fraction:
y + 42 = 4y + 6
Subtracting "y" from both sides:
42 = 3y + 6
Subtracting 6 from both sides:
36 = 3y
Dividing by 3:
y = 12
Now we can use either of the original equations to solve for "x". Let's use the expression we found for "x" in terms of "y":
x = y + 42
x = 12 + 42
x = 54
So the two numbers are 12 and 54.

Question 10

A company laid off 80% of its work force. The number of employees after the layoff is 3,000. How many employees were there before the layoff?
A) 5,400
B) 7,200
C) 3,600
D) 15,000
E) 3,750

Accepted Answer

Let x be the original number of employees.
After laying off 80%, the company has 20% of the original number of employees, which is 0.2x.
We are given that 0.2x = 3,000.
Solving for x, we get x = 15,000.
Therefore, the original number of employees was 15,000.

Question 11

Sam has $20,000 to invest. He invested part at 5% and part at 6%. His investments earned $1,120 total interest for the year. How much did Sam invest at each rate?
A) $12,000; $8000
B) $10,000; $10,000
C) $6000; $14,000
D) $14,000; $6000
E) $8000; $12,000

Accepted Answer

The answer of Sam has $20,000 to invest. He invested...

Question 12

Anders has $35,000 to invest. He invested part at 5.5% and part at 7%. His investments earned $2,195 total interest for the year. How much did Anders invest at each rate?
A) $17,000; $18,000
B) $18,000; $17,000
C) $20,000; $15,000
D) $15,000; $20,000
E) $10,000; $25,000

Accepted Answer

The answer of Anders has $35,000 to invest. He invested...

Question 13

A project manager needs to allocate a staff of 460 employees to a 3-stage project. Stage 2 must have 20% more staff than Stage 1. Stage 3 required 50% more than Stage 2. Determine the number of employees needed for stage 1, 2 and 3 respectively.
A) Stage 1 = 115; Stage 2 = 138; Stage 3 = 207
B) Stage 1 = 120; Stage 2 = 120; Stage 3 = 320
C) Stage 1 = 320; Stage 2 = 120; Stage 3 = 120
D) Stage 1 = 207; Stage 2 = 115; Stage 3 = 138
E) Stage 1 = 200; Stage 2 = 100; Stage 3 = 60

Accepted Answer

Let the number of employees in Stage 1 be x. Stage 2 will then have 1.2x employees (20% more than Stage 1), and Stage 3 will have 1.5 * 1.2x = 1.8x employees (50% more than Stage 2). The total is x + 1.2x + 1.8x = 4x = 460, solving for x gives x = 115. Therefore, Stage 1 = 115, Stage 2 = 138 (1.2 * 115), and Stage 3 = 207 (1.8 * 115).

Question 14

Stavros sells gold and green fabric in his drapery store. He buys the same quantity of both each quarter for $18 per metre for the gold fabric and $20 for the green fabric. His last order totalled $2,290. The supplier has advised Stavros that the gold fabric will increase by 20% and the green fabric by 25%, and his total order for the next quarter will be $2813. How many metres of gold fabric does Stavros order each quarter?
A) 65
B) 56
C) 85
D) 55
E) 25

Accepted Answer

The answer of Stavros sells gold and green fabric in...

Question 15

What was the percent change in unit price when a box of tissues dropped from 200 to 150 tissues per box? (with no change in the price per box)?
A) 25%
B) 20%
C) 30%
D) 35%
E) 33.3%

Accepted Answer

The percent change in unit price can be found using the formula:

percent change = [(new value - old value)/old value] x 100%

In this case, the old value is 200 and the new value is 150. Plugging these values into the formula, we get:

percent change = [(150 - 200)/200] x 100%
percent change = (-50/200) x 100%
percent change = -0.25 x 100%
percent change = -25%

However, we are asked for the percent change in unit price, not the percent change in quantity. Since there was no change in the price per box, the percent change in unit price is equal to the percent change in quantity, but with a positive sign. So:

percent change in unit price = |percent change in quantity| = |-25%| = 25%

Therefore, the answer is E.

Question 16

What was the percent change in unit price when a box of tissues dropped from 400 to 350 tissues per box? (with no change in the price per box)?
A) 12.5%
B) 15%
C) 17.5%
D) 11.7%
E) 14.3%

Accepted Answer

To find the percent change, we use the formula:

percent change = (new value - old value) / old value * 100%

Substituting in the given values, we get:

percent change = (350 - 400) / 400 * 100% = -50 / 400 * 100% = -12.5%

Note that the answer is negative because the unit price decreased. However, we want the absolute value of the percent change, so we take the positive value, which is 12.5%.

Therefore, the closest option to this value is E) 14.3%, which is the best choice.

Question 17

John and Jill agree to form a partnership. The partnership agreement requires that John invests $7,000.00 less than one-half of what Jill is to invest. If the total investment of both is $125,000.00, how much is Jill's investment?
A) $88,000.00
B) $37,000.00
C) $78,666.67
D) $46,333.33
E) $74,393.33

Accepted Answer

Let Jill's investment be $x$. According to the problem, John invests $\frac{1}{2}x - 7,000$. The total investment is $x + \frac{1}{2}x - 7,000 = 125,000$. Solving this equation gives Jill's investment as $88,000.00.

Question 18

At a United Way fund raiser, students sold cinnamon buns for $2 each or 3 for $5. They sold 500 all together, and raised $900. How many of the 3 for $5 were sold?
A) 100
B) 200
C) 300
D) 250
E) 150

Accepted Answer

The answer of At a United Way fund raiser, students...

Question 19

The stock market index decreased this month by one-thirteenth of last month's index. If this month's index is 2,400, what was last month's index?
A) 2,585
B) 2,320
C) 2,483
D) 2,600
E) 2,215

Accepted Answer

The decrease was one-thirteenth of last month's index, so this month's index is 12/13 of last month's index. To find last month's index, divide this month's index by 12/13: 2400 / (12/13) = 2600.

Question 20

The retail price of a packaged CD is $60.00, which includes a markup of 150% of cost. What is the cost price of the CD?
A) $40
B) $24
C) $36
D) $20
E) $32

Accepted Answer

Let's assume that the cost price (C) is x.
The markup percentage (MU%) is given as 150% or 1.5 
We know that the formula for calculating the markup is: 
Markup (MU%) = (Selling Price - Cost Price) / Cost Price * 100
Here, we can substitute MU% as 1.5 and selling price (SP) as 60.
1.5 = (60 - x) / x * 100
150 = 6000 - 100x
100x = 6000 - 150
x = 60 - 1.5 = 58.5
Hence, the cost price of the CD is $58.5.
Therefore, the best choice is B, which is $24 (rounded to the nearest dollar).

Quiz 2: B: Review and Applications of Algebra

If actual sales of $18,000 were 36% of budgeted sales, what were the budgeted sales?

An employee earns $1,562.50 for 55 hours of work during last week. His regular workweek is 40 hours and he gets overtime at time and one-half the regular rate of pay. What is the regular hourly rate of pay?

The commission on a transaction is 3% of the first $100,000 and 2% of the balance. What was the amount of a transaction where the commission charged was $10,100?

Bart purchased three-quarters of a 32% interest in a Swiss Chalet franchise for $270,000. What is implied value of the franchise?

A moving company charges an hourly rate plus a per kilometer rate. Sam paid $128.50 for his rental, having traveled 77Km over a 6 hour period. Taylor paid $205 for her rental, having traveled 140 km over a nine hour period. Determine the hourly rate and per Km rate charged by the rental company.

Tickets for the school play were $3 for students and $5 for all others. The box office sold 750 tickets for a total of $3,200. How many student tickets were sold?

It takes 40 minutes to produce product A and 60 minutes to produce product B. Last week 60 hours were used in manufacturing both products. A total of 70 units were produced. Determine the number of product A and B produced.

The difference between two numbers is 42. If one-half of the larger number is three more than twice the smaller number, what are the two numbers?

A company laid off 80% of its work force. The number of employees after the layoff is 3,000. How many employees were there before the layoff?

Sam has $20,000 to invest. He invested part at 5% and part at 6%. His investments earned $1,120 total interest for the year. How much did Sam invest at each rate?

Anders has $35,000 to invest. He invested part at 5.5% and part at 7%. His investments earned $2,195 total interest for the year. How much did Anders invest at each rate?

A project manager needs to allocate a staff of 460 employees to a 3-stage project. Stage 2 must have 20% more staff than Stage 1. Stage 3 required 50% more than Stage 2. Determine the number of employees needed for stage 1, 2 and 3 respectively.

What was the percent change in unit price when a box of tissues dropped from 200 to 150 tissues per box? (with no change in the price per box) ?

What was the percent change in unit price when a box of tissues dropped from 400 to 350 tissues per box? (with no change in the price per box) ?

John and Jill agree to form a partnership. The partnership agreement requires that John invests $7,000.00 less than one-half of what Jill is to invest. If the total investment of both is $125,000.00, how much is Jill's investment?

At a United Way fund raiser, students sold cinnamon buns for $2 each or 3 for $5. They sold 500 all together, and raised $900. How many of the 3 for $5 were sold?

The stock market index decreased this month by one-thirteenth of last month's index. If this month's index is 2,400, what was last month's index?

The retail price of a packaged CD is $60.00, which includes a markup of 150% of cost. What is the cost price of the CD?