Question 1

Solve.
-Center City East Parking Garage has a capacity of 257 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage.

Accepted Answer

Let the capacity of Center City West be x. Then, Center City East is x + 257. The equation is x + (x + 257) = 1221. Solving gives x = 482, so Center City West is 482 cars and Center City East is 739 cars.

Question 2

Solve.
-To trim the edges of a rectangular table cloth, 30 feet of lace are needed. The length of the table cloth is exactly one-half its width. What are the dimensions of the table cloth?

Accepted Answer

The answer of Solve.
-To trim the edges of a rectangular...

Question 3

Solve.
-A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $50 under this promotional deal, how many minutes of phone
Calls did he make? Round to the nearest integer, if necessary.

Accepted Answer

First, subtract the basic fee from the total bill: $50 - $15 = $35. Then, divide the remaining amount by the per-minute charge: $35 / $0.05 = 700 minutes.

Question 4

Solve.
-Mario's front patio is in the shape of a trapezoid with a height of 50 feet. The longer base is 11 feet longer than the shorter base, and the area of the patio is 10,000 square feet. Find the length of each Base of the trapezoidal patio.

Accepted Answer

The area of a trapezoid is given by the formula A = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases and h is the height. We are given that the area of the patio is 10,000 square feet and the height is 50 feet. We are also given that the longer base is 11 feet longer than the shorter base. Let x be the length of the shorter base. Then the length of the longer base is x + 11. Substituting these values into the formula for the area of a trapezoid, we get:10,000 = (1/2) * (x + x + 11) * 5010,000 = (1/2) * (2x + 11) * 5010,000 = (2x + 11) * 2510,000 = 50x + 2759,725 = 50xx = 194.5Therefore, the length of the shorter base is 194.5 feet and the length of the longer base is 194.5 + 11 = 205.5 feet.

Question 5

Solve.
-A number subtracted from 12 amounts to the quotient of 20 and -2. Find the number.

Accepted Answer

The quotient of 20 and -2 is -10. So, the equation is 12 - x = -10. Solving for x gives x = 22.

Question 6

Solve.
-The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $270,000, find each worker's salary.

Accepted Answer

Let the department head's salary be x. Then, the president's salary is 3x. The total salary is x + 3x = 4x = $270,000. Solving for x gives x = $67,500 (department head's salary), and 3x = $202,500 (president's salary).

Question 7

Solve.
-Nine times the sum of a number and -45 amounts to 108. Find the number.

Accepted Answer

Nine times the sum of a number and -45 amounts to 108.9(x - 45) = 108x - 45 = 12x = 57

Question 8

Solve.
-During an intramural basketball game, Team A scored 14 fewer points than Team B. Together, both teams scored a total of 146 points. How many points did Team A score during the game?

Accepted Answer

The answer of Solve.
-During an intramural basketball game, Team A...

Question 9

Solve.
-The difference of a number and 3 is the same as 49 less the number. Find the number.

Accepted Answer

The answer of Solve.
-The difference of a number and 3...

Question 10

Solve.
-The perimeter of a triangle is 50 centimeters. Find the lengths of its sides, if the longest side is 8 centimeters longer than the shortest side, and the remaining side is 3 centimeters longer than the
Shortest side.

Accepted Answer

Let the shortest side be x cm. Then the longest side is x + 8 cm, and the remaining side is x + 3 cm. The perimeter equation is x + (x + 8) + (x + 3) = 50. Solving gives x = 13. Thus, the sides are 13 cm, 16 cm, and 21 cm.

Question 11

Solve.
-30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in
The first bag, find the number of marbles in each bag.

Accepted Answer

The answer of Solve.
-30 marbles are to be divided into...

Question 12

Solve.
-Seven times some number added to 4 amounts to -12 added to the product of 3 and the number.

Accepted Answer

Let the number be x. The equation is 7x + 4 = 3x - 12. Solving for x gives x = -4.

Question 13

Solve.
-Two angles are complementary if their sum is $90 ^ { \circ }$. If the measure of the first angle is $x ^ { \circ }$, and the measure of the second angle is $( 3 x - 2 ) ^ { \circ }$, find the measure of each angle.

Accepted Answer

Since the angles are complementary, their sum equals $90^\circ$. Setting up the equation $x + (3x - 2) = 90$ and solving for $x$ gives $x = 23$, making the first angle $23^\circ$ and the second angle $67^\circ$.

Question 14

Solve.
-A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.19 per mile. If you rent this car for 2 days, how many whole miles can you drive if you only have $200 to spend.

Accepted Answer

The total cost for 2 days is 2 * $29.95 = $59.90. Subtracting this from $200 gives $140.10 for mileage. Dividing $140.10 by $0.19 per mile gives approximately 737 miles.

Question 15

Solve.
-The length of a rectangular room is 3 feet longer than twice the width. If the room's perimeter is 126 feet, what are the room's dimensions?

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 3 feet longer than twice the width ($w$), we can express the length as $l = 2w + 3$. Substituting this into the perimeter formula with $P = 126$ feet gives $126 = 2(2w + 3) + 2w$. Solving this equation for $w$ gives $w = 20$ feet. Substituting $w = 20$ feet back into the expression for the length gives $l = 2(20) + 3 = 43$ feet. Therefore, the dimensions are width = 20 ft and length = 43 ft.

Question 16

Solve.
-A 10-ft. board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Accepted Answer

The equation based on the given information is $x + (3x + 2) = 10$. Solving for $x$ gives $x = 2$, so the shorter piece is 2 ft and the longer piece is $3(2) + 2 = 8$ ft.

Question 17

Solve.
-Nine times a number, added to 5 , is $- 31$. Find the number.

Accepted Answer

The equation is $9x + 5 = -31$. Subtracting 5 from both sides gives $9x = -36$. Dividing both sides by 9 gives $x = -4$.

Question 18

Solve.
-Four times the sum of some number plus 2 is equal to 8 times the number minus 16.

Accepted Answer

The equation can be set up as 4(x + 2) = 8x - 16. Simplifying, we get 4x + 8 = 8x - 16. Subtracting 4x from both sides gives 8 = 4x - 16. Adding 16 to both sides gives 24 = 4x. Dividing both sides by 4 gives x = 6.

Question 19

Solve.
-Five times a number, added to 24 , is 54 . Find the number.

Accepted Answer

The equation is $5x + 24 = 54$. Subtracting 24 from both sides gives $5x = 30$. Dividing both sides by 5 gives $x = 6$.

Question 20

Solve.
-Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has. Together they have 105 foreign coins. Find how many coins Mary has.

Accepted Answer

Mary has 70 coins. If Mary has twice the number of coins John has, let John's coins be x. Then Mary's coins are 2x. Together, they have x + 2x = 3x = 105 coins. Solving for x gives x = 35 (John's coins), so Mary has 2x = 70 coins.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve. -Center City East Parking Garage has a capacity of 257 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage.

Solve. -To trim the edges of a rectangular table cloth, 30 feet of lace are needed. The length of the table cloth is exactly one-half its width. What are the dimensions of the table cloth?

Solve. -A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $50 under this promotional deal, how many minutes of phone Calls did he make? Round to the nearest integer, if necessary.

Solve. -Mario's front patio is in the shape of a trapezoid with a height of 50 feet. The longer base is 11 feet longer than the shorter base, and the area of the patio is 10,000 square feet. Find the length of each Base of the trapezoidal patio.

Solve. -A number subtracted from 12 amounts to the quotient of 20 and -2. Find the number.

Solve. -The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $270,000, find each worker's salary.

Solve. -Nine times the sum of a number and -45 amounts to 108. Find the number.

Solve. -During an intramural basketball game, Team A scored 14 fewer points than Team B. Together, both teams scored a total of 146 points. How many points did Team A score during the game?

Solve. -The difference of a number and 3 is the same as 49 less the number. Find the number.

Solve. -The perimeter of a triangle is 50 centimeters. Find the lengths of its sides, if the longest side is 8 centimeters longer than the shortest side, and the remaining side is 3 centimeters longer than the Shortest side.

Solve. -30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in The first bag, find the number of marbles in each bag.

Solve. -Seven times some number added to 4 amounts to -12 added to the product of 3 and the number.

Solve. -Two angles are complementary if their sum is $90 ^ { \circ }$ . If the measure of the first angle is $x ^ { \circ }$ , and the measure of the second angle is $( 3 x - 2 ) ^ { \circ }$ , find the measure of each angle.

Solve. -A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.19 per mile. If you rent this car for 2 days, how many whole miles can you drive if you only have $200 to spend.

Solve. -The length of a rectangular room is 3 feet longer than twice the width. If the room's perimeter is 126 feet, what are the room's dimensions?

Solve. -A 10-ft. board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Solve. -Nine times a number, added to 5 , is $- 31$ . Find the number.

Solve. -Four times the sum of some number plus 2 is equal to 8 times the number minus 16.

Solve. -Five times a number, added to 24 , is 54 . Find the number.

Solve. -Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has. Together they have 105 foreign coins. Find how many coins Mary has.