Question 1

Solve the problem.
-Angle A and angle B are supplementary angles and angle A is 15° less than four times angle B. Find the measures of angle A and angle B. 
A) A = 147°, B = 33°
B) A = 125°, B = 55°
C) A = 141°, B = 39°
D) A = 156°, B = 24°

Accepted Answer

Let x be the measure of angle B.

Angle A is 15 less than four times angle B, so:
A = 4x - 15

Angle A and angle B are supplementary, so:
A + B = 180

Substitute A with 4x-15: 
4x-15 + x = 180

Simplify and solve for x:
5x - 15 = 180 
5x = 195 
x = 39

Therefore, 
A = 4x - 15 = 141

The measures of angle A and angle B are 141° and 39° respectively, which matches the answer choice C. Let x be the measure of angle B.
Since angle A is 15° less than four times angle B, we have:
A = 4x - 15
Since angle A and angle B are supplementary, their sum is 180°. Therefore:
A + B = 180
Substituting A = 4x - 15, we get:
4x - 15 + x = 180
Simplifying this equation, we get:
5x = 195
x = 39
Substituting x = 39 back into A = 4x - 15, we get:
A = 141
Therefore, the measures of angle A and angle B are 141° and 39° respectively, and the answer is choice C.

Question 2

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-On a road trip, five friends drove at 50 miles per hour to California. On the way home, they took the same route but drove 75 miles per hour. How many miles did they drive on the way to California if the round trip took 10
Hours?
A) 600 miles
B) 6 miles
C) 1500 miles
D) 300 miles

Accepted Answer

Let the distance the friends drove on the way to California be d. Then, the distance they drove on the way back is also d.

We know that the total time of the round trip is 10 hours. We can set up an equation using the formula: distance = rate x time

d/50 + d/75 = 10

To solve for d, we can simplify the equation by finding a common denominator:

(3d + 2d)/150 = 10

5d/150 = 10

d = 300 miles

Therefore, the answer is D. Let's call the distance they traveled to California "x" (in miles).

We can use the formula:

time = distance / speed

On the way to California:

time = x / 50

On the way back:

time = x / 75

The total time for the round trip is given as 10 hours:

total time = time to California + time back

10 = x/50 + x/75

To solve for x, we'll need to first find a common denominator:

10 = 3x/150 + 2x/150

10 = 5x/150

Multiplying both sides by 150:

1500 = 5x

x = 300

Therefore, the answer is D) 300 miles.

Question 3

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Melita Zuba made a $600,000 cash contribution to two charities, the American Brain Tumor Association and the National Brain Tumor Foundation. The amount received by the National Brain Tumor Foundation was 20%
Greater than the amount received by the American Brain Tumor Association. How much did the American
Brain Tumor Association receive?
A) $327,272.73
B) $600,000
C) $272,727.27
D) $500,000.00

Accepted Answer

Let x be the amount received by the American Brain Tumor Association.
Then, the amount received by the National Brain Tumor Foundation is x + 0.20x = 1.2x.

The sum of these two amounts is $600,000, so:

x + 1.2x = $600,000
2.2x = $600,000
x = $272,727.27

Therefore, the American Brain Tumor Association received $272,727.27, which is option C). Let x be the amount received by the American Brain Tumor Association.

Then, the amount received by the National Brain Tumor Foundation is:

x + 0.2x = 1.2x

The total amount contributed is $600,000, so:

x + 1.2x = $600,000

Simplifying:

2.2x = $600,000

x = $272,727.27

Therefore, the American Brain Tumor Association received $272,727.27.

Question 4

Solve the problem.
-In a parallelogram, each of the two larger angles is 30° less than twice the smaller angles. Find the measure of each angle.
A) smaller angles = 50°; larger angles = 130°
B) smaller angles = 70°; larger angles = 110°
C) smaller angles = 10°; larger angles = 170°
D) smaller angles = 52.5°; larger angles = 127.5°

Accepted Answer

In a parallelogram, opposite angles are equal, and the sum of adjacent angles is 180°. Let the smaller angle be x. Then the larger angle is 2x - 30°. Since x + (2x - 30°) = 180°, solving gives x = 70° and the larger angle as 110°.

Question 5

Solve the problem.
-A bookcase is to be constructed with three shelves as shown. The height of the bookcase is 6 feet longer than the length of a shelf, and only 30 feet of lumber is available. What should be the width and height of the bookcase? 
A) length = 3 feet; height = 18 feet
B) length = 4.5 feet; height = 10.5 feet
C) length = 3 feet; height = 9 feet
D) length = 12 feet; height = 13.5 feet

Accepted Answer

The answer of Solve the problem.
-A bookcase is to be...

Question 6

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Because the budget cutbacks, MaryAnn was required to take a 19% pay cut. If she earned $51,000 before the pay cut, find her salary after the pay cut.
A) $50,903.10
B) $41,310
C) $4131
D) $50,031

Accepted Answer

Let x be MaryAnn's salary after the pay cut.

Since she took a 19% pay cut, her new salary is 81% of her old salary:

0.81($51,000) = x

x = $41,310

Therefore, MaryAnn's salary after the pay cut is $41,310. Let x be MaryAnn's salary after the pay cut.

The equation we can use to solve this problem is:

x = 51,000 - 0.19(51,000)

x = 51,000 - 9,690

x = 41,310

Therefore, MaryAnn's salary after the pay cut is $41,310, which is answer choice B.

Question 7

Solve the problem.
-In an isosceles triangle, one angle is 33° greater than the other two angles. Find the measure of all three angles.
A) 57°, 57°, 66°
B) 36.8°, 36.8°, 106.5°
C) 49°, 49°, 82°
D) 33°, 33°, 114°

Accepted Answer

Let x be the measure of the two congruent angles.
Then the third angle is x + 33.
Since the sum of the angles in a triangle is 180 degrees, we have:
x + x + (x + 33) = 180
Simplifying this equation, we get:
3x + 33 = 180
Subtracting 33 from both sides, we get:
3x = 147
Dividing both sides by 3, we get:
x = 49
Therefore, the two congruent angles are each 49 degrees and the third angle is 33 degrees greater, or 82 degrees.
So the measure of all three angles is 49 degrees, 49 degrees, and 82 degrees. Let x be the measure of each of the two equal angles in the isosceles triangle. Then the third angle is x + 33. The sum of the angles in a triangle is 180 degrees, so we have x + x + (x + 33) = 180. Simplifying the left side of the equation gives us 3x + 33 = 180. Solving for x we get x = 49. Therefore, the three angles are 49°, 49°, and 82°. So, the correct option is C.

Question 8

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Khang and Hector live 45.9 miles apart. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is 70% of Khang's. They start out at the same time and meet 3 hours later. Find
Hector's rate of speed.
A) 6.3 mph
B) 27 mph
C) 9 mph
D) 45.9 mph

Accepted Answer

The answer of Set up an equation that can be...

Question 9

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 3 hours on the road. Doreen can maintain a speed of 4.8 miles per hour, which is 40% of Irena's
Speed. If they meet exactly as planned, what is the distance between their houses?
A) 50.4 miles
B) 36 miles
C) 20.16 miles
D) 14.4 miles

Accepted Answer

First, find Irena's speed: 4.8 miles/hour / 40% = 12 miles/hour. The total distance covered in 3 hours is (4.8 + 12) miles/hour * 3 hours = 50.4 miles.

Question 10

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Alexander and Judy are 26 miles apart on a calm lake paddling toward each other. Alexander paddles at 3 miles per hour, while Judy paddles at 6 miles per hour. How long will it take them to meet?
A) 8.7 hours
B) 2.9 hours
C) 17 hours
D) 2.8 hours

Accepted Answer

The total distance they need to cover is 26 miles. Since they are moving towards each other, you can add their speeds together. Alexander paddles at 3 mph and Judy at 6 mph, making a combined speed of 9 mph. To find the time, divide the total distance by the combined speed: $ \frac{26 \text{ miles}}{9 \text{ mph}} = 2.888... $ hours, which rounds to 2.9 hours.

Question 11

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Train A leaves a station traveling at 32 km/h. Two hours later, train B leaves the same station traveling in the same direction at 52 km/h. How long does it takes train B to catch up to train A?
A) 3.2 hours
B) 4.2 hours
C) 5.2 hours
D) 2.2 hours

Accepted Answer

Let's use the formula:

distance = rate * time

Distance that train A travels before train B catches up is the same distance that train B travels after it catches up. Let's call this distance "D".

For train A:

D = 32 * (t + 2)

where t is the time train B takes to catch up.

For train B:

D = 52 * t

Setting both equations equal to each other:

32 * (t + 2) = 52 * t

Simplifying and solving for t:

32 * t + 64 = 52 * t

20 * t = 64

t = 3.2

So it takes train B 3.2 hours to catch up to train A.

Therefore, the answer is C) 5.2 hours. Let's use the formula:
distance = speed x time
Let's call the time it takes for train B to catch up to train A "t".
When train B catches up to train A, they will have traveled the same distance.
So, the distance that train A travels in "t" hours is:
distance A = 32km/h x (t + 2h) (remember, train A left 2 hours earlier)
The distance that train B travels in "t" hours is:
distance B = 52km/h x t
Since they travel the same distance when train B catches up to train A, we can set the two equations equal to each other:
32km/h x (t + 2h) = 52km/h x t
32t + 64 = 52t
20t = 64
t = 3.2 hours
Therefore, it takes train B 3.2 hours to catch up to train A.
The best choice is C.

Question 12

Solve the problem.
-The perimeter of a rectangular room is 174 feet. Find the length and width of the room if the length is 9 feet longer than twice the width.
A) w = 31 ft; l = 71 ft
B) w = 52 ft; l = 122 ft
C) w = 26 ft; l = 61 ft
D) w = 39 ft; l = 48 ft

Accepted Answer

Let's call the width of the room "w" and the length "l". We can set up two equations based on the given information:
Perimeter = 2(length + width)
174 = 2(l + w)
l = 9 + 2w  (since "the length is 9 feet longer than twice the width")
Now we can substitute the second equation into the first equation and solve for w:
174 = 2(9 + 3w)
87 = 9 + 3w
78 = 3w
w = 26
To find the length, we can plug in w = 26 to the equation l = 9 + 2w:
l = 9 + 2(26)
l = 61
Therefore, the width is 26 feet and the length is 61 feet, making choice C the best answer. Let w be the width of the room.
Then the length of the room is 2w+9.
The perimeter of the room is 2(length + width) = 2(2w+9 + w) = 6w+18.
So we have the equation 6w+18 = 174.
Solving for w, we get w = 26.
So the width of the room is 26 feet, and the length is 2w+9 = 2(26)+9 = 61 feet.
Therefore, the answer is C, w = 26 ft; l = 61 ft.

Question 13

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A motorcycle traveling at 60 miles per hour overtakes a car traveling at 30 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles?
A) 60 miles
B) 6 miles
C) 180 miles
D) 3 miles

Accepted Answer

Let d be the distance from the starting point. 
Then, the car had traveled for 3 hours at 30 mph and traveled a distance of 90 miles (d = 30*3). 
When the motorcycle overtakes the car, it travels the same distance as the car plus some additional distance d, which is the distance between the two vehicles at that moment. 
Using the formula d = rt, we have:
d = 60t (distance traveled by the motorcycle) 
d = 30(t+3) (distance traveled by the car, which includes the three-hour head start) 
Setting these two equations equal to each other, we get: 
60t = 30(t+3) 
Solving for t, we get t=3. 
Substituting t=3 back into one of the equations (e.g. d = 60t), we get d=180 miles. 
Therefore, Choice C is the correct answer. Let d be the distance from the starting point.

The car travels for 3 hours before the motorcycle overtakes it, so the car has already covered 3 * 30 = 90 miles.

When the motorcycle overtakes the car, it has traveled the same distance as the car plus some additional distance d:

60t = 30t + 90 + d

where t is the time after the car started.

Simplifying the equation, we get:

30t = 90 + d

We know that the motorcycle overtakes the car, so they travel the same distance d.

Therefore, we can equate the two expressions for d:

60t = 30t + 90 + d

d = 30t + 90

d = 30(t + 3)

Now we need to find the value of d by finding the value of t.

Since the motorcycle overtakes the car, we know that it travels for less time than the car:

t < 3

Also, we know that both vehicles travel the same distance d:

60t = 30t + 90 + d

60t = 30t + 90 + 30(t + 3)

60t = 60t + 180

0 = 180

This is impossible, so there is no solution to the equation for t.

However, we can use the equation for d:

d = 30(t + 3)

Since t < 3, the maximum value of t + 3 is 6, which occurs when t = 3.

Therefore, the maximum value of d is 30 * 6 = 180 miles.

Thus, the answer is C) 180 miles.

Question 14

Solve the problem.
-The measure of one angle of a quadrilateral is three times the smallest angle; the third angle is 12° greater than the smallest angle; and the fourth angle is 70° less than twice the second angle.
A) angle 1 = 46.4°; angle 2 = 139.3°; angle 3 = 151.3°; angle 4 = 22.9°
B) angle 1 = 52.3°; angle 2 = 104.5°; angle 3 = 64.3°; angle 4 = 139°
C) angle 1 = 59.7°; angle 2 = 179.1°; angle 3 = 71.7°; angle 4 = 49.4°
D) angle 1 = 38°; angle 2 = 114°; angle 3 = 50°; angle 4 = 158°

Accepted Answer

Let x be the smallest angle.
- First angle = 3x
- Second angle = x + 12
- Fourth angle = 2(x + 12) - 70 = 2x - 26
The sum of the angles of a quadrilateral is 360°.
3x + x + 12 + 2x - 26 = 360
6x - 14 = 360
6x = 374
x ≈ 62.3
Therefore:
- First angle ≈ 186.9
- Second angle ≈ 74.3
- Third angle ≈ 74.3 + 12 = 86.3
- Fourth angle ≈ 2(74.3) - 70 = 78.6
These values are closest to the angles in choice D.

Question 15

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 10 miles per hour. How long will it be until they are 29 miles apart from
Each other?
A) 1.9 hours
B) 5.8 hours
C) 0.5 hours
D) 0.6 hours

Accepted Answer

The distance between Linda and Dave increases at a combined rate of 5 mph + 10 mph = 15 mph. To find the time until they are 29 miles apart, divide the distance by their combined rate: 29 miles / 15 mph = 1.933 hours, which rounds to 1.9 hours.

Question 16

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Jeff starts driving at 55 miles per hour from the same point that Lauren starts driving at 40 miles per hour. They drive in opposite directions, and Lauren has a half-hour head start. How long will they be able to talk on their
Cell phones that have a 290-mile range?
A) 3 hours
B) 3.1 hours
C) 3.3 hours
D) 2.8 hours

Accepted Answer

The answer of Set up an equation that can be...

Question 17

Solve the problem.
-Angle A and angle B are complementary angles and angle A is 10° more than three times angle B. Find the measures of angle A and angle B. 
A) A = 20°, B = 70°
B) A = 30°, B = 60°
C) A = 60°, B = 30°
D) A = 70°, B = 20°

Accepted Answer

The answer of Solve the problem.
-Angle A and angle B...

Question 18

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-The local clothing store marks up the price that it pays to the clothing manufacturer by 30%. If the selling price of a pair of jeans is $105, how much did the clothing store pay for the jeans?
A) $150.00
B) $26.25
C) $136.50
D) $80.77

Accepted Answer

The store marks up the price by 30%, meaning the selling price is 130% of the cost price. Let x be the cost price. The equation is 1.3x = $105. Solving for x gives x = $105 / 1.3 = $80.77.

Question 19

Solve the problem.
-A rectangular horse pen is to be fenced and divided into five partitions as shown. The length of the fenced-in area is to be twice the width, and the total amount of fencing to be used is 390 feet. Find the length and width of
The fenced-in area. 
A) l = 78 ft, w = 39 ft
B) l = 41 ft, w = 39 ft
C) l = 27.9 ft, w = 14 ft
D) l = 86.7 ft, w = 43.3 ft

Accepted Answer

The answer of Solve the problem.
-A rectangular horse pen is...

Question 20

Solve the problem.
-
A) 48°
B) 21.2°
C) 157°
D) 138°

Accepted Answer

The given string of characters is not a mathematical problem, it cannot be solved. It is likely a code or identification number. Therefore, none of the answer choices provided are correct.

Quiz 3: Applications of Algebra

Solve the problem. -Angle A and angle B are supplementary angles and angle A is 15° less than four times angle B. Find the measures of angle A and angle B.

Solve the problem. -In a parallelogram, each of the two larger angles is 30° less than twice the smaller angles. Find the measure of each angle.

Solve the problem. -A bookcase is to be constructed with three shelves as shown. The height of the bookcase is 6 feet longer than the length of a shelf, and only 30 feet of lumber is available. What should be the width and height of the bookcase?

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -Because the budget cutbacks, MaryAnn was required to take a 19% pay cut. If she earned $51,000 before the pay cut, find her salary after the pay cut.

Solve the problem. -In an isosceles triangle, one angle is 33° greater than the other two angles. Find the measure of all three angles.

Solve the problem. -The perimeter of a rectangular room is 174 feet. Find the length and width of the room if the length is 9 feet longer than twice the width.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -A motorcycle traveling at 60 miles per hour overtakes a car traveling at 30 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles?

Solve the problem. -The measure of one angle of a quadrilateral is three times the smallest angle; the third angle is 12° greater than the smallest angle; and the fourth angle is 70° less than twice the second angle.

Solve the problem. -Angle A and angle B are complementary angles and angle A is 10° more than three times angle B. Find the measures of angle A and angle B.

Solve the problem. -A rectangular horse pen is to be fenced and divided into five partitions as shown. The length of the fenced-in area is to be twice the width, and the total amount of fencing to be used is 390 feet. Find the length and width of The fenced-in area.

Solve the problem. -