Algebra Practice Test 1

  1. If Lynn can type a page in \(p\) minutes, what piece of the page can she do in five minutes?
  1. \(\frac{5}{p}\)
  2. \(p-5\)
  3. \(p+5\)
  4. \(\frac{p}{5}\)
  5. \(1-p+5\)
Show Answer
The correct answer is A!

The following proportion may be written:

\(\frac{1}{p}=\frac{x}{5}\)

Solving for the variable \(x\) gives \(xp = 5\), where \(x=\frac{5}{p}\). So, Lynn can type \(\frac{5}{p}\) pages in five minutes.

 

  1. If Sally can paint a house in four hours, and John can paint the same house in six hours, how long will it take for both of them to paint the house together?
  1. 2 hours and 24 minutes
  2. 3 hours and 12 minutes
  3. 3 hours and 44 minutes
  4. 4 hours and 10 minutes
  5. 4 hours and 33 minutes
Show Answer
The correct answer is A!

Sally can paint \(\frac{1}{4}\) of the house in one hour. John can paint \(\frac{1}{6}\) of the same house in one hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written:

\(\frac{1}{4}x+\frac{1}{6}x=1\)

Solving for \(x\) gives \(\frac{5}{12}x=1\), where \(x\) is 2.4 hours, which is 2 hours and 24 minutes.

 

  1. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15%-off sale, how much will he pay if the dishwasher originally cost $450?
  1. $280.90
  2. $287
  3. $292.50
  4. $306
  5. $333.89
Show Answer
The correct answer is D!

First, apply the 15% sale discount to the original price. Fifteen percent of 450 is 67.50, so the sales price is:

\($450-$67.50=$382.50\)

Next, the employee discount is 20% off the sale price. Twenty percent of 382.50 is 76.50, so the final cost is:

\($382.50-$76.50=$306\)

 

  1. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
  1. $14,310.40
  2. $14,990.90
  3. $15,290.70
  4. $15,737.50
  5. $16,935.80
Show Answer
The correct answer is D!

A 20% discount means you pay 80% of the original price. Let the original price be \(x\):

\(0.8x = $12,590\)

Divide both sides by 0.8 to solve for \(x\):

\(x=\frac{$12,590}{0.8}=$15,737.50\)

 

  1. Solve the following equation for \(A\):
\(\frac{2A}{3} = 8 + 4A\)
  1. –2.4
  2. 2.4
  3. 1.3
  4. –1.3
  5. 0
Show Answer
The correct answer is A!

In order to solve for \(A\), both sides of the equation may first be multiplied by 3. This is written as \(3 \times \frac{2A}{3}=3(8+4A)\) or \(2A=24+12A\). Subtraction of \(12A\) from both sides of the equation gives \(-10A=24\). Division by -10 gives \(A = -2.4\).

 

  1. Leah is 6 years older than Sue, John is 5 years older than Leah, and the total of their ages is 41. How old is Sue?
  1. 8
  2. 10
  3. 14
  4. 19
  5. 21
Show Answer
The correct answer is A!

Let Sue’s age be \(s\). Since Leah is 6 years older, Leah’s age is \(s + 6\). John is 5 years older than Leah, so John’s age is \((s + 6) + 5 = s + 11\).

Their total age is \(s + (s + 6) + (s + 11) = 41\).

Combine like terms:

\(3s + 17 = 41\)

Subtract 17:

\(3s = 24\)

Finally, divide by 3:

\(s = 8\)

 

  1. Alfred wants to invest $4,000 at 6% simple interest rate for five years. How much interest will he receive?
  1. $240
  2. $480
  3. $720
  4. $960
  5. $1,200
Show Answer
The correct answer is E!

Simple interest is represented by the formula \(I = Prt\), where \(P\) represents the principal amount, \(r\) represents the interest rate, and \(t\) represents the time.

Substituting $4,000 for \(P\), 0.06 for \(r\), and 5 for \(t\) gives \(I = 4,000 \times 0.06 \times 5\), or \(I = 1,200\). So, he will receive $1,200 in interest.

 

  1. Jim is able to sell a hand-carved statue for $670, which was a 35% profit over his cost. How much did the statue originally cost him?
  1. $496.30
  2. $512.40
  3. $555.40
  4. $574.90
  5. $588.20
Show Answer
The correct answer is A!

A 35% profit means the selling price is 135% of the cost. To find the cost, divide the selling price by 1.35:

\(\text{Cost}= \frac{670}{1.35} \approx 496.30\)

 

  1. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much from this stay will the city receive in taxes?
  1. 10 cents
  2. 11 cents
  3. 15 cents
  4. 17 cents
  5. 21 cents
Show Answer
The correct answer is D!

The amount of taxes is equal to \($55 \times 0.003\), or $0.165. Rounding to the nearest cent gives 17 cents.

 

  1. A student receives his grade report from a local community college, but the GPA is smudged. He took a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a “B” in the art class, an “A” in the history class, a “C” in the science class, a “B” in the mathematics class, and an “A” in the science lab. What was his GPA if the letter grades are based on a 4-point scale?
Grading scale: A=4, B=3, C=2, D=1, F=0.
  1. 2.7
  2. 2.8
  3. 3.0
  4. 3.1
  5. 3.2
Show Answer
The correct answer is C!

The GPA may be calculated by writing the following expression:

\(\frac{(3\times2)+(4\times3)+(2\times4)+(3\times3)+(4\times1)}{13}\)

This equals 3.0.

 

  1. Simon arrived at work at 8:15 a.m. and left work at 10:30 p.m. If Simon gets paid by the hour at a rate of $10 and time and a half for any hours worked over eight in a day, how much did Simon get paid?
  1. $120.25
  2. $160.75
  3. $173.75
  4. $180.00
  5. $182.50
Show Answer
The correct answer is C!

From 8:15 a.m. to 4:15 p.m., he gets paid $10 per hour, with the total amount paid represented by the following equation:

\($10 \times 8=$80\)

From 4:15 p.m. to 10:30 p.m., he gets paid $15 per hour, with the total amount paid represented by the following equation:

\($15 \times 6.25=$93.75\)

The sum of $80 and $93.75 is $173.75, so he was paid $173.75 for 14.25 hours of work.

 

  1. Grace has 16 jelly beans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jelly beans she must take out of her pocket to ensure that she has one of each color?
  1. 4
  2. 8
  3. 12
  4. 13
  5. 16
Show Answer
The correct answer is D!

If she removes 13 jelly beans from her pocket, she will have 3 jelly beans left, with each color represented. If she removes only 12 jelly beans, green or blue may not be represented.

 

  1. If \(r = 5z\) and \(15z = 3y\), then \(r =\) ?
  1. \(y\)
  2. \(2y\)
  3. \(4y\)
  4. \(10y\)
  5. \(15y\)
Show Answer
The correct answer is A!

The value of \(z\) may be determined by dividing both sides of the equation \(r=5z\) by 5. Doing so gives \(\frac{r}{5}=z\).

Substituting \(\frac{r}{5}\) for the variable \(z\) in the equation \(15z=3y\) gives \(15 \times \frac{r}{5}=3y\).

Solving for \(y\) gives \(r = y\).

 

  1. If 300 jelly beans cost you \(x\) dollars, how many jelly beans can you purchase for 50 cents at the same rate?
  1. \(\frac{150}{x}\)
  2. \(150x\)
  3. \(6x\)
  4. \(\frac{1,500}{x}\)
  5. \(600x\)
Show Answer
The correct answer is A!

50 cents is half of one dollar, thus the ratio is written as half of 300, or 150, to \(x\). The equation representing this situation is:

\(\frac{300}{x}\times \frac{1}{2}=\frac{150}{x}\)

 

  1. Kirstin worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?
  1. $57
  2. $90
  3. $104
  4. $112
  5. $122
Show Answer
The correct answer is B!

The following proportion may be used to determine how much Lee will make next week:

\(\frac{22}{132}=\frac{15}{x}\)

Solving for \(x\) gives \(x = 90\). Thus, she will make $90 next week if she works 15 hours.

 

  1. If \(8x + 5x + 2x + 4x = 114\), then \(5x + 3 =\) ?
  1. 12
  2. 25
  3. 33
  4. 47
  5. 86
Show Answer
The correct answer is C!

The given equation should be solved for \(x\). Doing so gives \(x = 6\). Substituting the \(x\)-value of 6 into the expression \(5x + 3\) gives \(5(6) + 3\), which is 33.

 

  1. You need to purchase a textbook for nursing school. The book cost $80, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?
  1. $5.20
  2. $7.35
  3. $13.40
  4. $19.95
  5. $21.25
Show Answer
The correct answer is C!

The amount you will pay for the book may be represented by the expression \(80+(80 \times 0.0825)\). Thus, you will pay $86.60 for the book. The change you will receive is equal to the difference of $100 and $86.60, which is $13.40.

 

  1. You purchase a car, and have made a down payment of $3,000 and six monthly payments of $225. How much have you paid so far for the car?
  1. $3,225
  2. $4,350
  3. $5,375
  4. $6,550
  5. $6,398
Show Answer
The correct answer is B!

The amount you have paid for the car may be written as \($3,000 + 6($225)\), which equals $4,350.

 

  1. Your supervisor instructs you to purchase 240 pens and six staplers for the nurse’s station. Pens are purchased in sets of six for $2.35 per pack. Staplers are sold in sets of two for 12.95. How much will purchasing these products cost?
  1. $132.85
  2. $145.75
  3. $162.90
  4. $225.25
  5. $226.75
Show Answer
The correct answer is A!

You will need 40 packs of pens and three sets of staplers. Thus, the total cost may be represented by the expression \(40(2.35) + 3(12.95)\). The total cost is $132.85.

 

  1. If \(y = 3\), then \(y^3(y^3-y)=\) ?
  1. 300
  2. 459
  3. 648
  4. 999
  5. 1,099
Show Answer
The correct answer is C!

Substituting 3 for \(y\) gives \(33 (33-3)\), which equals \(27(27 – 3)\), or \(27(24)\). Thus, the expression equals 648.