Question 1

Solve.
-Jan swims at a speed of 4.9 mph in still water. The river she's in flows at a speed of 3.4 mph. How long will it take Jan to swim 1.3 mi downstream? Round your answer to the nearest tenth of an hour, if necessary.

Accepted Answer

To solve this problem, we can use the formula:
time = distance / speed

Since Jan is swimming downstream (with the current), her effective speed will be the sum of her swimming speed and the speed of the river flow.

Effective speed downstream = swimming speed + river flow speed
= 4.9 mph + 3.4 mph
= 8.3 mph

Now we can use the formula to find the time it will take Jan to swim 1.3 miles downstream:

time = distance / speed
= 1.3 miles / 8.3 mph
≈ 0.1566 hours
≈ 0.2 hours (rounded to the nearest tenth of an hour)

Therefore, it will take Jan about 0.2 hours (or 12 minutes) to swim 1.3 miles downstream. The best choice is C. To solve this problem, we can use the formula: 
time = distance / (swim speed + river speed)

Substituting the given values, we get: 
time = 1.3 mi / (4.9 mph + 3.4 mph) = 0.2 hr

Rounding to the nearest tenth, we get the final answer of 0.2 hours, which is equivalent to approximately 12 minutes. Therefore, the best choice is C.

Question 2

Solve.
-At the end of the day, a storekeeper had $1498 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount that is the tax.

Accepted Answer

The sales tax is 7% of the total sales. So, the amount of tax is 0.07 * 1498 = $98.

Question 3

Solve.
-A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 24 inches more than the width. What are the dimensions of the carpet?

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 24 inches more than the width ($l = w + 24$), and the perimeter is 232 inches, we can set up the equation $232 = 2(w + 24) + 2w$. Solving this equation for $w$ gives us $w = 46$ inches, and thus $l = 70$ inches.

Question 4

Solve.
-A salesperson earned $300 a week plus a bonus of $16 for each service contract sold. If the pay one week was $428 how many service contracts were sold?

Accepted Answer

The salesperson's total pay minus the base pay ($428 - $300 = $128) divided by the bonus per contract ($16) equals 8 contracts.

Question 5

Solve.
-Midtown Antiques collects 5% sales tax on all sales. If total sales including tax are $1808.58, find the portion that is the tax. Round your answer to the nearest cent.

Accepted Answer

Let the portion that is the tax be x.
Then we have: 
Total sales including tax = sales price + tax
$1808.58 = sales price + 0.05(sales price)
$1808.58 = 1.05(sales price)
sales price = $1722.46
So the tax is:
x = total sales including tax - sales price
x = $1808.58 - $1722.46
x = $86.12
Therefore, the answer is B) $86.12. Let's assume that the portion of the sales before tax is x.
Then, the tax collected would be 5% of x, which is 0.05x.
So, we have:
x + 0.05x = 1808.58 (total sales including tax)
Simplifying this:
1.05x = 1808.58
x = 1722.46
So, the portion that is the tax is:
0.05x = 0.05(1722.46) = $86.12 (rounded to the nearest cent)
Therefore, the answer is B.

Question 6

Solve.
-A plane traveling 390 mph in still air encounters a 60-mph headwind. How long will it take the plane to travel 660 mi into the wind? Round your answer to the nearest tenth of an hour, if necessary.

Accepted Answer

The plane's effective speed into the wind is 390 mph - 60 mph = 330 mph. To travel 660 miles at this speed, it would take 660 miles / 330 mph = 2 hours.

Question 7

Solve.
-In a local election, 26,400 people voted. This was an increase of 5% over the last election. How many people voted in the last election? Round your answer to the nearest whole number of people.

Accepted Answer

To find the number of people who voted in the last election, divide the current number of voters by 1.05 (since a 5% increase means the current number is 105% of the last election's number). So, 26,400 / 1.05 = 25,142.857, which rounds to 25,143 people.

Question 8

Solve.
-In a local election, 36,100 people voted. This was a decrease of 13% less than the last election. How many people voted in the last election? Round your answer to the nearest whole number of people.

Accepted Answer

To find the number of people who voted in the last election, divide the current number of voters by (1 - 0.13). So, 36,100 / 0.87 = 41,494 people.

Question 9

Solve.
-The following is a real estate commission on the selling price of a house. 10% for the first $100,000, and
2% for the amount which exceeds $100,000
A realtor receives $13,480.00 for selling a house. What was the selling price?

Accepted Answer

The commission is $10,000 for the first $100,000 (10% of $100,000) and $3,480 for the remaining amount (2% of $174,000), totaling $13,480. Thus, the selling price is $100,000 + $174,000 = $274,000.

Question 10

Solve.
-After receiving a discount of 13.5% on its bulk order of toner cartridges, John's Office Supply pays $6574. What was the price of the order before the discount?

Accepted Answer

Let x be the price of the order before the discount.

After the discount of 13.5%, the price becomes:

x - 0.135x = 0.865x

We know that 0.865x = $6574, so:

x = $7600

Therefore, the price of the order before the discount was $7600.

The answer is choice (C) $7600.

Question 11

Solve.
-A speedboat moves at a rate of 24 km/hr in still water. How long will it take someone to ride the boat 136 km upstream if the river's current moves at a rate of 7 km/hr?

Accepted Answer

The speed of the boat in still water is 24 km/hr, and the speed of the river's current is 7 km/hr. When moving upstream, the effective speed of the boat is the difference between these two speeds, which is 24 km/hr - 7 km/hr = 17 km/hr. To find the time it takes to travel 136 km upstream, divide the distance by the effective speed: 136 km / 17 km/hr = 8 hours.

Question 12

Solve.
-If the first and third of three consecutive odd integers are added, the result is 81 less than five times the second integer. Find the third integer.

Accepted Answer

Let x be the second odd integer. Then the first and third are x-2 and x+2 respectively. According to the problem,
(x-2) + (x+2) = 5x - 81
Simplifying this equation gives x = 29, which is the second odd integer. Therefore, the third odd integer is x+2= 31. Hence, the answer is D) 29.

Question 13

Solve.
-Bill swims at a speed of 6.1 mph in still water. The river he's in flows at a speed of 2.3 mph. How long will it take Bill to swim 2.1 mi upstream? Round your answer to the nearest tenth of an hour, if necessary.

Accepted Answer

When swimming upstream, Bill's effective speed is 6.1 mph - 2.3 mph = 3.8 mph. To find the time, divide the distance by the speed: 2.1 mi / 3.8 mph ≈ 0.5526 hours, which rounds to 0.6 hours.

Question 14

Solve.
-A speedboat moves at a rate of 24 km/hr in still water. How long will it take someone to ride the boat 87 km downstream if the river's current moves at a rate of 5 km/hr?

Accepted Answer

The speedboat's speed downstream will be the sum of its speed in still water and the speed of the current, which is:
24 km/hr + 5 km/hr = 29 km/hr

Using the formula distance = speed x time, we can solve for the time it will take to travel 87 km downstream:
time = distance / speed
time = 87 km / 29 km/hr
time = 3 hours

Therefore, the answer is choice C, 3 hours. Let's denote the time it takes to ride the boat downstream as $t$. 
Since the boat is traveling downstream, we need to add the speed of the river's current to the speed of the boat to get the total speed:
$24 	ext{ km/hr} + 5 	ext{ km/hr} = 29 	ext{ km/hr}$
This means that the boat is traveling 29 km every hour downstream.
To find how long it takes for the boat to travel 87 km downstream, we divide the distance by the speed:
$ \frac{87 	ext{ km}}{29 	ext{ km/hr}} = 3 	ext{ hours}$
Therefore, the answer is C) 3 hr.

Question 15

Solve.
-A pie-shaped (triangular)lake-front lot has a perimeter of 1300 feet. One side is 300 feet longer than the shortest side, while the third side is 400 feet longer than the shortest side. Find the lengths of all three sides.

Accepted Answer

Let the shortest side be x feet. Then, the other sides are x + 300 feet and x + 400 feet. The perimeter is the sum of all sides, so x + (x + 300) + (x + 400) = 1300. Solving this equation, we get x = 200 feet. Therefore, the sides are 200 ft, 500 ft (200 + 300), and 600 ft (200 + 400).

Question 16

Solve.
-In a triangular cross-section of a lean-to for water fowl in an aviary, the second angle is 3 times as large as the first angle. The measure of the third angle is 10° greater than that of the first angle. How large are the angles?

Accepted Answer

Let x be the measure of the first angle.
Then the measure of the second angle is 3x.
And the measure of the third angle is x+10.
The sum of the angles in a triangle is 180°, so we have:
x + 3x + (x+10) = 180
5x + 10 = 180
5x = 170
x = 34
Therefore, the first angle is 34°, the second angle is 3x34 = 102°, and the third angle is x+10 = 44°.
Thus, the best choice is A. Let x be the measure of the first angle. Then, the second angle is 3x and the third angle is x + 10.

Since the sum of the angles in a triangle is 180°, we can write an equation:

x + 3x + (x + 10) = 180

Simplifying the equation, we get:

5x + 10 = 180

5x = 170

x = 34

Therefore, the angles are:

First angle = x = 34°
Second angle = 3x = 102°
Third angle = x + 10 = 44°

So, the best choice is A.

Question 17

Solve.
-On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 8%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1566?

Accepted Answer

The investor sold the shares for $1566 after they increased by 8%. To find the original price, divide $1566 by 1.08, which equals $1450.

Question 18

Solve.
-If Gloria received a 3 percent raise and is now making $24,720 a year, what was her salary before the raise?

Accepted Answer

Gloria's new salary is the result of a 3% raise, so her salary before the raise was 100% of her original salary. To find the original salary, divide her new salary by 1.03 (100% + 3% = 103%, or 1.03 in decimal form). $24,720 / 1.03 = $24,000.

Question 19

Solve.
-Stevie bought a stereo for $300 and put it on sale at his store at a 65% markup rate. What was the retail price of the stereo?

Accepted Answer

To find the retail price, we need to add the markup to the original price.
Markup = 65% of $300 = 0.65 x $300 = $195
Retail price = Original price + Markup = $300 + $195 = $495 Markup rate = 65%
Cost price = $300
Markup amount = 65% of $300 = $195
Selling price = Cost price + Markup amount
Selling price = $300 + $195 = $495
Therefore, the retail price of the stereo was $495. Option D is the correct answer.

Question 20

Solve.
-Suppose the sales of a particular brand of appliance satisfy the relationship S = 170x + 2300, where S represents the number of appliances sold in year x, with x = 0 corresponding to 1982. Find the number of appliances sold
In 1997.

Accepted Answer

To determine the number of appliances sold in 1997, we need to find the value of S when x=15 (since 1997 is 15 years after 1982).

S = 170x + 2300 
S = 170(15) + 2300 
S = 2550 + 2300 
S = 4850

Therefore, the number of appliances sold in 1997 was 4850. The correct choice is B.

Quiz 1: Solving Linear Equations and Inequalities

Solve. -Jan swims at a speed of 4.9 mph in still water. The river she's in flows at a speed of 3.4 mph. How long will it take Jan to swim 1.3 mi downstream? Round your answer to the nearest tenth of an hour, if necessary.

Solve. -At the end of the day, a storekeeper had $1498 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount that is the tax.

Solve. -A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 24 inches more than the width. What are the dimensions of the carpet?

Solve. -A salesperson earned $300 a week plus a bonus of $16 for each service contract sold. If the pay one week was $428 how many service contracts were sold?

Solve. -Midtown Antiques collects 5% sales tax on all sales. If total sales including tax are $1808.58, find the portion that is the tax. Round your answer to the nearest cent.

Solve. -A plane traveling 390 mph in still air encounters a 60-mph headwind. How long will it take the plane to travel 660 mi into the wind? Round your answer to the nearest tenth of an hour, if necessary.

Solve. -In a local election, 26,400 people voted. This was an increase of 5% over the last election. How many people voted in the last election? Round your answer to the nearest whole number of people.

Solve. -In a local election, 36,100 people voted. This was a decrease of 13% less than the last election. How many people voted in the last election? Round your answer to the nearest whole number of people.

Solve. -The following is a real estate commission on the selling price of a house. 10% for the first $100,000, and 2% for the amount which exceeds $100,000 A realtor receives $13,480.00 for selling a house. What was the selling price?

Solve. -After receiving a discount of 13.5% on its bulk order of toner cartridges, John's Office Supply pays $6574. What was the price of the order before the discount?

Solve. -A speedboat moves at a rate of 24 km/hr in still water. How long will it take someone to ride the boat 136 km upstream if the river's current moves at a rate of 7 km/hr?

Solve. -If the first and third of three consecutive odd integers are added, the result is 81 less than five times the second integer. Find the third integer.

Solve. -Bill swims at a speed of 6.1 mph in still water. The river he's in flows at a speed of 2.3 mph. How long will it take Bill to swim 2.1 mi upstream? Round your answer to the nearest tenth of an hour, if necessary.

Solve. -A speedboat moves at a rate of 24 km/hr in still water. How long will it take someone to ride the boat 87 km downstream if the river's current moves at a rate of 5 km/hr?

Solve. -A pie-shaped (triangular) lake-front lot has a perimeter of 1300 feet. One side is 300 feet longer than the shortest side, while the third side is 400 feet longer than the shortest side. Find the lengths of all three sides.

Solve. -In a triangular cross-section of a lean-to for water fowl in an aviary, the second angle is 3 times as large as the first angle. The measure of the third angle is 10° greater than that of the first angle. How large are the angles?

Solve. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 8%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1566?

Solve. -If Gloria received a 3 percent raise and is now making $24,720 a year, what was her salary before the raise?

Solve. -Stevie bought a stereo for $300 and put it on sale at his store at a 65% markup rate. What was the retail price of the stereo?

Solve. -Suppose the sales of a particular brand of appliance satisfy the relationship S = 170x + 2300, where S represents the number of appliances sold in year x, with x = 0 corresponding to 1982. Find the number of appliances sold In 1997.