Question 1

Solve.
-It took Sara's mother 4 hours round trip to drive to the University and bring Sara back home for spring break. If the University is 88 miles from home, find her mother's average speed.

Accepted Answer

The total distance for the round trip is 2 times 88 miles, which equals 176 miles. Since it took 4 hours for the round trip, the average speed is 176 miles / 4 hours = 44 mph.

Question 2

Solve.
-Use the formula C = $\frac { 5 } { 9 }$ (F(F - 32)to write 95° F as degrees Celsius.

Accepted Answer

The answer of Solve.
-Use the formula C = \(\frac {...

Question 3

Solve the problem.
-Center City East Parking Garage has a capacity of 252 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1216 cars, find the capacity for each garage.

Accepted Answer

Let the capacity of Center City West Parking Garage be $x$. Then, the capacity of Center City East Parking Garage is $x + 252$. The combined capacity is $x + (x + 252) = 1216$. Solving for $x$, we get $2x + 252 = 1216$, so $2x = 964$, and $x = 482$. Therefore, Center City West has a capacity of 482 cars, and Center City East has a capacity of $482 + 252 = 734$ cars.

Question 4

Solve the problem.
-A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

Accepted Answer

For 3 days of rental, the cost without including the miles would be 3 x $29.95 = $89.85. This leaves $200 - $89.85 = $110.15 for miles. To find how many miles can be driven for $110.15, divide $110.15 by $0.29 per mile: $110.15/$0.29 per mile = 379 miles. Therefore, the answer is Choice C, 379 miles. The cost of renting the car for 3 days is:
$29.95/day x 3 days = $89.85
This leaves $110.15 ($200 - $89.85) to spend on miles.
To figure out how many miles you can drive for $110.15, you can set up the equation:
0.29x = 110.15
where x is the number of miles you can drive.
Solving for x gives:
x = 379.48
Since you can only drive whole miles, the maximum number of miles you can drive is 379 miles.

Therefore, the best choice is C.

Question 5

Solve the problem.
-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 $170,000, find each worker's salary.

Accepted Answer

Let x be the department head's salary, then the president's salary is 3x. The total of their salaries is x + 3x = 4x, which is given to be $170,000. Solving for x, we get x = $42,500 for the department head's salary, and 3x = $127,500 for the president's salary. Thus, the correct answer is choice C. Let x be the department head's salary.
Then the president's salary is 3x.
The total of their salaries is $170,000, so we have:
x + 3x = $170,000
4x = $170,000
x = $42,500
So the department head's salary is $42,500 and the president's salary is 3 times that, or $127,500. Therefore, the answer is C.

Question 6

Solve the problem.
-Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has. Together they have 90 foreign coins. Find how many coins Mary has.

Accepted Answer

Mary has twice the number of coins that John has, so if John has x coins, Mary has 2x coins. Together, they have x + 2x = 3x coins, which equals 90. Solving 3x = 90 gives x = 30 (John's coins), so Mary has 2x = 60 coins.

Question 7

Solve.
-Use the formula F = $\frac { 9 } { 5 } \mathrm { C }$  + 32 to write 15° C as degrees Fahrenheit.

Accepted Answer

To convert 15°C to Fahrenheit, use the formula F = (9/5)C + 32. Substituting 15 for C gives F = (9/5)*15 + 32 = 59°F.

Question 8

Solve the problem.
-Two angles are complementary if their sum is 90°. If the measure of the first angle is x°, and the measure of the second angle is (3x - 2)°, find the measure of each angle.

Accepted Answer

We know that two angles are complementary if their sum is 90°.
So, x + (3x - 2) = 90°
Simplifying the equation:
4x - 2 = 90°
4x = 92°
x = 23°
Therefore, the measure of the first angle is 23° and the measure of the second angle is (3x - 2) = 67°. So, the answer is choice D.

Question 9

Solve.
-You have taken up gardening for relaxation and have decided to fence in your new rectangular shaped masterpiece. The length of the garden is 2 meters and 46 meters of fencing is required to completely enclose it.
What is the width of the garden?

Accepted Answer

The perimeter of a rectangle is given by 2(length + width). Given the length is 2 meters and the perimeter is 46 meters, we can set up the equation: 2(2 + width) = 46. Solving for width gives width = 21 meters.

Question 10

Solve the problem.
-During an intramural basketball game, Team A scored 14 fewer points than Team B. Together, both teams scored a total of 148 points. How many points did Team A score during the game?

Accepted Answer

The answer of Solve the problem.
-During an intramural basketball game,...

Question 11

Solve.
-The code to unlock a safety deposit box is three consecutive odd integers whose sum is 87. Find the integers.

Accepted Answer

The sum of three consecutive odd integers can be represented as (x) + (x+2) + (x+4) = 87. Solving for x gives x = 27, so the integers are 27, 29, and 31.

Question 12

Solve the problem.
-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 $51 under this promotional deal, how many minutes of phone calls did he make? Round to
The nearest integer, if necessary.

Accepted Answer

To find the number of minutes Joe made phone calls, we first subtract the basic fee from the total bill: $51 - $15 = $36. Then, we divide the remaining amount by the per-minute charge: $36 / $0.05 = 720 minutes.

Question 13

Solve.
-The sum of three consecutive integers is 588. Find the numbers.

Accepted Answer

The sum of three consecutive integers can be represented as x + (x+1) + (x+2) = 588. Simplifying gives 3x + 3 = 588, so 3x = 585, and x = 195. Therefore, the integers are 195, 196, and 197.

Question 14

Solve.
-A number subtracted from 11 yields the quotient of 42 and 7. Find the number.

Accepted Answer

The quotient of 42 and 7 is 6, so the equation can be written as 11 - x = 6. Solving for x, we get x = 5. Therefore, the answer is choice C. The problem can be written as:
11 - x = 6
Solving for x gives x = 5
Therefore, the answer is choice C)5.

Question 15

Solve.
-Sally is making a cover for a round table. When finished, the cover will fit exactly with no excess hanging off. Sally has to cut the fabric circle with a 4 inch larger diameter than the table to allow for hemming. If the table
Has a diameter of 66 inches, how much fabric does Sally need? (Use 3.14 for.14 for $\pi$ . R. Round to 2 decimal places.)

Accepted Answer

The answer of Solve.
-Sally is making a cover for a...

Question 16

Solve.
-In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 90 and the U.S. won
More than China who won more than Romania, how many medals did each team win?

Accepted Answer

Let x be the number of medals won by Romania. Then, the number of medals won by China is x+1 and the number of medals won by the U.S. is x+2 (since the U.S. won more than China who won more than Romania). The sum of the three consecutive integers is 3x+3, which is equal to 90. Therefore, 3x+3=90 or 3x=87. Solving for x, we get x=29, which means Romania won 29 medals, China won 30 medals, and the U.S. won 31 medals. Thus, the answer is D. Let the number of medals won by Romania be x. Then, China won x + 1 medals and the U.S. won x + 2 medals. The sum of these three integers is 3x + 3, which is equal to 90 according to the problem. Therefore, 3x + 3 = 90, which simplifies to 3x = 87 and x = 29. Hence, Romania won 29 medals, China won 30 medals, and the U.S. won 31 medals. Therefore, the correct answer is D.

Question 17

Solve the problem.
-In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 84 and the U.S. won
More than China who won more than Romania, how many medals did each team win?

Accepted Answer

The sum of three consecutive integers that equals 84 can be found by dividing 84 by 3 to find the middle number, which is 28. Therefore, the three numbers are 27, 28, and 29. Since the U.S. won the most, followed by China, then Romania, the distribution is U.S.: 29 medals, China: 28 medals, Romania: 27 medals.

Question 18

Solve.
-The house numbers of two adjacent homes are two consecutive even numbers. If their sum is 330, find the house numbers.

Accepted Answer

Let x be the smaller even number (house number) and x+2 be the larger even number (house number). Then we have:
x + (x+2) = 330
2x + 2 = 330
2x = 328
x = 164
So the smaller even number is 164 and the larger even number is 166, which are the house numbers of the two adjacent homes. Therefore, the answer is B. Let's call the house numbers x and x+2 (since they are consecutive even numbers). 
We know that x + (x+2) = 330 (since their sum is 330). 
Simplifying this equation, we get: 
2x + 2 = 330 
2x = 328 
x = 164 
So one house number is 164, and the other is 166 (since they are consecutive even numbers). 
Therefore, the answer is B)164, 166.

Question 19

Solve the problem.
-A 6-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

If the shorter piece is x feet, then the longer piece is 3x + 2 feet. The equation is x + (3x + 2) = 6. Solving gives x = 1, so the shorter piece is 1 ft and the longer piece is 5 ft.

Question 20

Solve.
-Ted drove to his grandparents' house for a holiday weekend. The total distance (one-way)was 371 miles and it took him 5 hours. How fast was Ted driving? (Round answer to the nearest whole number)

Accepted Answer

To calculate Ted's speed, we need to use the formula:
Speed = Distance / Time
Since the total distance was 371 miles and it took him 5 hours, we can plug in these values to get:
Speed = 371 / 5
Speed = 74.2 mph
Rounding to the nearest whole number, we get:
Speed ≈ 74 mph To find Ted's speed, we need to divide the distance he traveled by the time it took him:
Speed = Distance / Time
Speed = 371 miles / 5 hours
Speed = 74.2 mph
Rounded to the nearest whole number, Ted was driving 74 mph, which corresponds to answer choice D.

Quiz 9: Equations, Inequalities, and Problem Solving

Solve. -It took Sara's mother 4 hours round trip to drive to the University and bring Sara back home for spring break. If the University is 88 miles from home, find her mother's average speed.

Solve. -Use the formula C = $\frac { 5 } { 9 }$ (F(F - 32) to write 95° F as degrees Celsius.

Solve the problem. -Center City East Parking Garage has a capacity of 252 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1216 cars, find the capacity for each garage.

Solve the problem. -A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

Solve the problem. -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 $170,000, find each worker's salary.

Solve the problem. -Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has. Together they have 90 foreign coins. Find how many coins Mary has.

Solve. -Use the formula F = $\frac { 9 } { 5 } \mathrm { C }$ + 32 to write 15° C as degrees Fahrenheit.

Solve the problem. -Two angles are complementary if their sum is 90°. If the measure of the first angle is x°, and the measure of the second angle is (3x - 2) °, find the measure of each angle.

Solve. -You have taken up gardening for relaxation and have decided to fence in your new rectangular shaped masterpiece. The length of the garden is 2 meters and 46 meters of fencing is required to completely enclose it. What is the width of the garden?

Solve the problem. -During an intramural basketball game, Team A scored 14 fewer points than Team B. Together, both teams scored a total of 148 points. How many points did Team A score during the game?

Solve. -The code to unlock a safety deposit box is three consecutive odd integers whose sum is 87. Find the integers.

Solve the problem. -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 $51 under this promotional deal, how many minutes of phone calls did he make? Round to The nearest integer, if necessary.

Solve. -The sum of three consecutive integers is 588. Find the numbers.

Solve. -A number subtracted from 11 yields the quotient of 42 and 7. Find the number.

Solve. -In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 90 and the U.S. won More than China who won more than Romania, how many medals did each team win?

Solve. -The house numbers of two adjacent homes are two consecutive even numbers. If their sum is 330, find the house numbers.

Solve the problem. -A 6-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. -Ted drove to his grandparents' house for a holiday weekend. The total distance (one-way) was 371 miles and it took him 5 hours. How fast was Ted driving? (Round answer to the nearest whole number)