Question 1

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-If three times the smaller of two consecutive integers is added to four times the larger, the result is 109. Find the smaller integer.
A) 45
B) 14
C) 16
D) 15

Accepted Answer

Let x be the smaller integer, then the larger integer is x+1. According to the problem, 3x+4(x+1)=109. Simplifying this equation gives 7x+4=109. Solving for x, we get x=15. Therefore, the smaller integer is 15.

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the measure of an angle such that the difference between its supplement and 3 times its complement is 6°. 
A) $24 ^ { \circ }$
B) $48 ^ { \circ }$
C) $152 ^ { \circ }$
D) $76 ^ { \circ }$

Accepted Answer

The supplement of an angle $x$ is $180 - x$ degrees, and the complement is $90 - x$ degrees. The equation based on the given problem is $180 - x - 3(90 - x) = 6$. Solving this equation gives $x = 48$ degrees.

Question 3

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A triangular lake-front lot has a perimeter of 1100 feet. One side is 300 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.
A) 200 feet, 500 feet, 700 feet
B) 100 feet, 200 feet, 300 feet
C) 200 feet, 200 feet, 200 feet
D) 100 feet, 400 feet, 600 feet

Accepted Answer

Let x be the length of the shortest side. Then the other sides are x + 300 and x + 500. Since the perimeter is 1100, we have x + (x + 300) + (x + 500) = 1100, which simplifies to 3x + 800 = 1100. Solving for x, we get x = 100. Therefore, the lengths of the three sides are 100, 400, and 600. Hence, the answer is D.

Question 4

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A rectangular Persian carpet has a perimeter of 176 inches. The length of the carpet is 18 inches more than the width. What are the dimensions of the carpet?
A) 79 inches, 97 inches
B) 70 inches, 88 inches
C) 35 inches, 53 inches
D) 53 inches, 71 inches

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 5

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the measure of an angle such that the sum of the measures of its complement and its supplement is 174°. 
A) $43 ^ { \circ }$
B) $48 ^ { \circ }$
C) $6 ^ { \circ }$
D) $3 ^ { \circ }$

Accepted Answer

The complement of an angle is 90 degrees minus the angle, and the supplement is 180 degrees minus the angle. If x is the angle, then its complement is $90 - x$ and its supplement is $180 - x$. The sum of the complement and supplement is $270 - 2x = 174$. Solving for x, $2x = 96$, so $x = 48$.

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A 9-pound puppy is gaining weight at a rate of $\frac { 2 } { 3 } \mathrm { lb }$ per week. How much more time will it take for the puppy's weight to exceed $28 \frac { 2 } { 3 } \mathrm { lb }$ ?
A) More than $1 \frac { 3 } { 4 }$ week(s)

B) More than $30 \frac { 1 } { 2 }$ weeks

C) More than $56 \frac { 1 } { 2 }$ weeks

D) More than $29 \frac { 1 } { 2 }$ weeks

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the measure of an angle whose supplement is 3 times the measure of its complement. 
A) $60 ^ { \circ }$
B) $45 ^ { \circ }$
C) $30 ^ { \circ }$
D) $22.5 ^ { \circ }$

Accepted Answer

Let x be the measure of the angle. 
The supplement of the angle is 180-x. 
The complement of the angle is 90-x. 
According to the problem, we have:
180-x = 3(90-x) 
Solving for x, we get:
x = 45 
Therefore, the angle measures $45 ^ { \circ }$.

Question 8

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The complement of an angle measures 52° less than the angle. Find the measure of the angle. 
A) $161 ^ { \circ }$
B) $71 ^ { \circ }$
C) $29 ^ { \circ }$
D) 128

Accepted Answer

The complement of an angle is 90 degrees minus the angle. If the complement is 52 degrees less than the angle, we can set up the equation: angle - 52 = 90 - angle. Solving this equation for the angle gives us 71 degrees.

Question 9

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the measure of an angle if its supplement measures 265° less than 6 times its complement. 
A) $82 ^ { \circ }$
B) $164 ^ { \circ }$
C) $19 ^ { \circ }$
D) $9 ^ { \circ }$

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 10

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A square plywood platform has a perimeter which is 6 times the length of a side, decreased by 8. Find the length of a side.
A) 4
B) 1
C) 6
D) 2

Accepted Answer

The perimeter of a square is 4 times the length of a side. If the perimeter is 6 times the length of a side minus 8, we can set up the equation 4s = 6s - 8. Solving for s, we subtract 6s from both sides to get -2s = -8, and then divide by -2 to find s = 4.

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A circle has a circumference of 26π meters. Find the radius of the circle.
A) 4 meters
B) 26 meters
C) 7 meters
D) 13 meters

Accepted Answer

The formula for the circumference of a circle is C=2πr, where C is the circumference and r is the radius.

We are given that the circumference of the circle is 26π meters. So,

26π = 2πr

Divide both sides by 2π:

13 = r

Therefore, the radius of the circle is 13 meters.

The correct answer is D).

Question 12

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Two angles of a triangle are 50° and 100°. What is the measure of the third angle? 
A) $210 ^ { \circ }$
B) $150 ^ { \circ }$
C) $- 60 ^ { \circ }$
D) $30 ^ { \circ }$

Accepted Answer

The sum of the angles in a triangle is always 180°. Given two angles are 50° and 100°, the third angle = 180° - (50° + 100°) = 30°.

Question 13

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the length of a rectangular lot with a perimeter of 136 meters if the length is 6 meters more than the width.
A) 31 meters
B) 74 meters
C) 68 meters
D) 37 meters

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 14

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-DGʹs Plumbing and Heating charges $50 plus $60 per hour for emergency service. Bill remembers being billed just over $200 for an emergency call. How long to the nearest hour was the plumber at
Billʹs house?
A) 11 hours
B) 13 hours
C) 4 hours
D) 3 hours

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 15

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find the measure of an angle, if its supplement measures 51° more than twice its complement. 
A) $39 ^ { \circ }$
B) $102 ^ { \circ }$
C) $61 ^ { \circ }$
D) $51 ^ { \circ }$

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 16

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-If the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. Find the third integer.
A) 19
B) 42
C) 23
D) 21

Accepted Answer

Let the first odd integer be x.
Then the next two consecutive odd integers are x+2 and x+4.
According to the problem, we have:
x + (x+4) = 5(x+2) - 63
Simplifying this equation gives:
2x + 4 = 5x - 53
Rearranging the equation gives:
3x = 57
Therefore, x = 19
So the three consecutive odd integers are 19, 21, and 23.
Thus, the third integer is 23.

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A car rental company has two rental rates. Rate 1 is $72 per day plus $0.18 per mile. Rate 2 is $144 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to
Drive to pay less by taking Rate 2?
A) More than 5600 miles
B) More than 39,900 miles
C) More than 78,400 miles
D) More than 19,600 miles

Accepted Answer

To find when Rate 2 becomes cheaper, set up the inequality: 7(72) + 0.18x > 7(144) + 0.09x. Solving gives x > 5600 miles.

Question 18

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The perimeter of a rectangular room is 196 feet. Find the length and width of the room if the length is 8 feet longer than twice the width.
A) width = 30 feet; length = 68 feet
B) width = 35 feet; length = 78 feet
C) width = 45 feet; length = 53 feet
D) width = 60 feet; length = 136 feet

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 (l) is 8 feet longer than twice the width (w), we can express this as l = 2w + 8. The perimeter is given as 196 feet, so substituting the expression for l into the perimeter formula gives 2(2w + 8) + 2w = 196. Simplifying this equation leads to the width being 30 feet and the length being 68 feet, which matches option A.

Question 19

Choose the one alternative that best completes the statement or answers the question.
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 250 feet. Find
The length and width of the fenced-in area.

A) length = 55.6 feet, width = 27.8 feet
B) length = 22.4 feet, width = 11.2 feet
C) length = 27 feet, width = 25 feet
D) length = 50 feet, width = 25 feet

Accepted Answer

Let the width of the fenced-in area be x. Then the length of the fenced-in area is 2x. There are five partitions, so the total length of fencing needed is the perimeter of the rectangular area plus twice the width. This gives:
250 = 2(2x + x) + 5x
Simplifying and solving for x, we get:
x = 25
So, the width is 25 feet and the length is 2(25) = 50 feet. Therefore, the answer is D.

Question 20

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A bag of marbles has twice as many blue marbles as green marbles, and the bag has at least 45 marbles in it. At least how many green marbles does it have?
A) At least 23 green marbles
B) At least 30 green marbles
C) At least 16 green marbles
D) At least 15 green marbles

Accepted Answer

Let the number of green marbles be $g$ and blue marbles be $2g$. The total number of marbles is at least 45, so $g + 2g \geq 45$, which simplifies to $3g \geq 45$. Solving for $g$, we get $g \geq 15$. Therefore, the bag has at least 15 green marbles.

Quiz 2: Linear Equations

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -If three times the smaller of two consecutive integers is added to four times the larger, the result is 109. Find the smaller integer.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle such that the difference between its supplement and 3 times its complement is 6°.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A rectangular Persian carpet has a perimeter of 176 inches. The length of the carpet is 18 inches more than the width. What are the dimensions of the carpet?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle such that the sum of the measures of its complement and its supplement is 174°.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle whose supplement is 3 times the measure of its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The complement of an angle measures 52° less than the angle. Find the measure of the angle.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle if its supplement measures 265° less than 6 times its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A square plywood platform has a perimeter which is 6 times the length of a side, decreased by 8. Find the length of a side.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A circle has a circumference of 26π meters. Find the radius of the circle.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Two angles of a triangle are 50° and 100°. What is the measure of the third angle?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the length of a rectangular lot with a perimeter of 136 meters if the length is 6 meters more than the width.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle, if its supplement measures 51° more than twice its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -If the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. Find the third integer.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The perimeter of a rectangular room is 196 feet. Find the length and width of the room if the length is 8 feet longer than twice the width.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A bag of marbles has twice as many blue marbles as green marbles, and the bag has at least 45 marbles in it. At least how many green marbles does it have?