- If Lynn can type a page in \(p\) minutes, what piece of the page can she do in five minutes?
- \(\frac{5}{p}\)
- \(p-5\)
- \(p+5\)
- \(\frac{p}{5}\)
- \(1-p+5\)
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.
- 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?
- 2 hours and 24 minutes
- 3 hours and 12 minutes
- 3 hours and 44 minutes
- 4 hours and 10 minutes
- 4 hours and 33 minutes
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.
- 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?
- $280.90
- $287
- $292.50
- $306
- $333.89
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:
\($382.50-$76.50=$306\)
- The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
- $14,310.40
- $14,990.90
- $15,290.70
- $15,737.50
- $16,935.80
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 \(x\):
\(x=\frac{$12,590}{0.8}=$15,737.50\)
- Solve the following equation for \(A\):
- –2.4
- 2.4
- 1.3
- –1.3
- 0
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 \(A = -2.4\).
- 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?
- 8
- 10
- 14
- 19
- 21
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:
\(s = 8\)
- Alfred wants to invest $4,000 at 6% simple interest rate for five years. How much interest will he receive?
- $240
- $480
- $720
- $960
- $1,200
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.
- 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?
- $496.30
- $512.40
- $555.40
- $574.90
- $588.20
A 35% profit means the selling price is 135% of the cost. To find the cost, divide the selling price by 1.35:
\(\text{Cost}= \frac{670}{1.35} \approx 496.30\)
- 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?
- 10 cents
- 11 cents
- 15 cents
- 17 cents
- 21 cents
The amount of taxes is equal to \($55 \times 0.003\), or $0.165. Rounding to the nearest cent gives 17 cents.
- 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?
- 2.7
- 2.8
- 3.0
- 3.1
- 3.2
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.
- 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?
- $120.25
- $160.75
- $173.75
- $180.00
- $182.50
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.
- 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?
- 4
- 8
- 12
- 13
- 16
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.
- If \(r = 5z\) and \(15z = 3y\), then \(r =\) ?
- \(y\)
- \(2y\)
- \(4y\)
- \(10y\)
- \(15y\)
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 \(r = y\).
- If 300 jelly beans cost you \(x\) dollars, how many jelly beans can you purchase for 50 cents at the same rate?
- \(\frac{150}{x}\)
- \(150x\)
- \(6x\)
- \(\frac{1,500}{x}\)
- \(600x\)
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:
\(\frac{300}{x}\times \frac{1}{2}=\frac{150}{x}\)
- 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?
- $57
- $90
- $104
- $112
- $122
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.
- If \(8x + 5x + 2x + 4x = 114\), then \(5x + 3 =\) ?
- 12
- 25
- 33
- 47
- 86
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.
- 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?
- $5.20
- $7.35
- $13.40
- $19.95
- $21.25
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.
- 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?
- $3,225
- $4,350
- $5,375
- $6,550
- $6,398
The amount you have paid for the car may be written as \($3,000 + 6($225)\), which equals $4,350.
- 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?
- $132.85
- $145.75
- $162.90
- $225.25
- $226.75
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.
- If \(y = 3\), then \(y^3(y^3-y)=\) ?
- 300
- 459
- 648
- 999
- 1,099
Substituting 3 for \(y\) gives \(33 (33-3)\), which equals \(27(27 – 3)\), or \(27(24)\). Thus, the expression equals 648.