Question 1

Solve the problem.
-Jay drove 308 kilometers at the average rate of 77 kilometers per hour. How long did the trip take?

Accepted Answer

The answer of Solve the problem.
-Jay drove 308 kilometers at...

Question 2

Solve the problem.
-Helen Weller invested $10,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments
Amounts to 11%?

Accepted Answer

The average return on the two investments is 11%. So, the total interest earned from both investments should be 11% of the total amount invested.The interest earned from the first investment is 10% of $10,000 = $1,000.Let x be the amount invested in the second account. The interest earned from the second investment is 13% of x = 0.13x.The total interest earned from both investments is $1,000 + 0.13x.The total amount invested is $10,000 + x.So, we have the equation:($1,000 + 0.13x) / ($10,000 + x) = 0.11Solving for x, we get:x = $6,000

Question 3

Solve the problem.
-Carl participates in a bowling tournament. After completing  of the games, his average score per game is 200. What must his average score be in the remaining games in order for his overall game average to be 223.33?
Round your answer to the nearest point.

Accepted Answer

The answer of Solve the problem.
-Carl participates in a bowling...

Question 4

Solve the problem.
-In the first two weeks of school, Jill studied 20 hours and 15 hours, respectively. How many hours must she study during the third week to give her an average of 20 hours per week?

Accepted Answer

To achieve an average of 20 hours per week over three weeks, Jill needs to study a total of 60 hours (20 hours/week * 3 weeks). She has already studied 35 hours (20 hours + 15 hours). Therefore, she needs to study an additional 25 hours in the third week.

Question 5

Solve the problem.
-Jill is 13.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 3 hours. How fast is Joe walking?

Accepted Answer

Jill walks 1.5 km/h for 3 hours, covering 4.5 km. The remaining distance Joe covers is 13.5 km - 4.5 km = 9 km in 3 hours, so Joe walks at 3 km/h.

Question 6

Solve the problem.
-Sarah and Shakina are running in a 4-lap, 1 mile race. Shakina is exactly one lap behind at the moment when Sarah completes her second lap. If Sarah averages 0.19 miles per minute for her last two laps, what must
Shakina's average speed be in order for her to just pull even with Sarah at the finish line?

Accepted Answer

Shakina needs to cover 3 laps (0.75 miles) in the same time Sarah covers 2 laps (0.5 miles) at 0.19 mi/min. Sarah takes 0.5 / 0.19 = 2.63 minutes to finish. Shakina's speed = 0.75 miles / 2.63 minutes = 0.29 mi/min.

Question 7

Solve the problem.
-A student earned scores of 85, 83, 90, 94, 88, and 84 on the first six tests in a biology class. What score is needed on the seventh test to produce an 86 average?

Accepted Answer

The answer of Solve the problem.
-A student earned scores of...

Question 8

Solve the problem.
-A bakery owner sells rectangular birthday cakes that are 5 inches longer than they are wide. To increase his profit, he decides to decrease both the length and width by 3 inches. If the area of the new cake is 66 in.2 smaller
Than the old cake, then what are the length and width of the old cake?

Accepted Answer

Let the width of the old cake be x inches, then the length is x + 5 inches. The area of the old cake is x(x + 5). The new dimensions are (x - 3) and (x + 2), with an area of (x - 3)(x + 2). The difference in area is 66, so x(x + 5) - (x - 3)(x + 2) = 66. Solving this equation gives x = 10, so the old dimensions are 15 inches by 10 inches.

Question 9

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 5 miles per hour and Delvis is traveling at the speed of 7 miles per hour. In 2 hours, what is the distance between them?

Accepted Answer

Delvis travels 2 miles per hour faster than Candy. Over 2 hours, the distance between them increases by 2 miles/hour * 2 hours = 4 miles.

Question 10

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 6 miles per hour. In how many hours will they be 48 miles apart?

Accepted Answer

The answer of Solve the problem.
-From a point on a...

Question 11

Solve the problem.
-Over the past two weeks, Jane earned $156 and $290 respectively, at her part time job. What must she earn in the third week to bring her three-week average earnings to $200 per week?

Accepted Answer

The answer of Solve the problem.
-Over the past two weeks,...

Question 12

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 18 inches across and requires 2.2 bags of concrete in order to fill it to ground level. What is the depth of the hole? Round
Your answer to the nearest inch. (One bag of concrete, when mixed with the appropriate amount of water,
Makes  of material.)

Accepted Answer

The answer of Solve the problem.
-A circular hole is filled...

Question 13

Solve the problem.
-An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 120 mph. On the return trip, the plane must fly against this wind, which decreases its normal speed by the same amount. The
Flight from Metro City takes 1.70 hours and the return trip takes 3.48 hours. How far is it from Metro City to
Gotham?

Accepted Answer

The plane's speed with the tailwind is 120 mph greater than its normal speed, and its speed against the headwind is 120 mph less than its normal speed. Let the normal speed be x mph. Then, the speed with the tailwind is (x + 120) mph, and the speed against the headwind is (x - 120) mph. The distance from Metro City to Gotham is the same on both trips, so we can set up the following equation:(x + 120) * 1.70 = (x - 120) * 3.48Solving for x, we get:x = 600 mphTherefore, the distance from Metro City to Gotham is:(600 + 120) * 1.70 = 1220 milesThe correct answer is A: 800 mi.

Question 14

Solve the problem.
-From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 10 miles per hour and Fred rides 13 miles per hour. In how many hours will they be 115 miles apart?

Accepted Answer

Since John and Fred are moving in opposite directions, their speeds add up. Together, they cover 10 + 13 = 23 miles per hour. To find out how long it will take them to be 115 miles apart, divide the total distance by their combined speed: 115 miles / 23 miles per hour = 5 hours.

Question 15

Solve the problem.
-A triangular lake-front lot has a perimeter of 1700 feet. One side is 100 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 + 100 feet and x + 400 feet. The perimeter is the sum of all sides, so x + (x + 100) + (x + 400) = 1700. Simplifying, 3x + 500 = 1700, so 3x = 1200, and x = 400. Therefore, the sides are 400 ft, 500 ft, and 800 ft.

Question 16

Solve the problem.
-From a point on a straight road, two cars are driven in opposite directions, one at 50 miles per hour and the other at 45 miles per hour. In how many hours will they be 475 miles apart?

Accepted Answer

Since the cars are moving in opposite directions, their speeds add up. Thus, the combined speed is 50 mph + 45 mph = 95 mph. To find the time, divide the total distance by the combined speed: 475 miles / 95 mph = 5 hours.

Question 17

Solve the problem.
-A rectangular Persian carpet has a perimeter of 248 inches. The length of the carpet is 28 inches more than the width. What are the dimensions of the carpet?

Accepted Answer

The answer of Solve the problem.
-A rectangular Persian carpet has...

Question 18

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 10 miles per hour. In how many hours will they be 57 miles apart?

Accepted Answer

The relative speed of the two boats is 9 + 10 = 19 miles per hour. To find the time it takes for them to be 57 miles apart, divide the distance by the relative speed: 57 miles ÷ 19 miles per hour = 3 hours.

Question 19

Solve the problem.
-Jim had grades of 67 and 88 on two chemistry tests. What is the lowest score he can get on the third test to maintain an average of 75?

Accepted Answer

The answer of Solve the problem.
-Jim had grades of 67...

Question 20

Solve the problem.
-Janet drove 325 kilometers and the trip took 5 hours. How fast was Janet traveling?

Accepted Answer

The answer of Solve the problem.
-Janet drove 325 kilometers and...

Quiz 1: Equations, Inequalities, and Modeling

Solve the problem. -Jay drove 308 kilometers at the average rate of 77 kilometers per hour. How long did the trip take?

Solve the problem. -Helen Weller invested $10,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments Amounts to 11%?

Solve the problem. -Carl participates in a bowling tournament. After completing of the games, his average score per game is 200. What must his average score be in the remaining games in order for his overall game average to be 223.33? Round your answer to the nearest point.

Solve the problem. -In the first two weeks of school, Jill studied 20 hours and 15 hours, respectively. How many hours must she study during the third week to give her an average of 20 hours per week?

Solve the problem. -Jill is 13.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 3 hours. How fast is Joe walking?

Solve the problem. -A student earned scores of 85, 83, 90, 94, 88, and 84 on the first six tests in a biology class. What score is needed on the seventh test to produce an 86 average?

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 5 miles per hour and Delvis is traveling at the speed of 7 miles per hour. In 2 hours, what is the distance between them?

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 6 miles per hour. In how many hours will they be 48 miles apart?

Solve the problem. -Over the past two weeks, Jane earned $156 and $290 respectively, at her part time job. What must she earn in the third week to bring her three-week average earnings to $200 per week?

Solve the problem. -From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 10 miles per hour and Fred rides 13 miles per hour. In how many hours will they be 115 miles apart?

Solve the problem. -A triangular lake-front lot has a perimeter of 1700 feet. One side is 100 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 the problem. -From a point on a straight road, two cars are driven in opposite directions, one at 50 miles per hour and the other at 45 miles per hour. In how many hours will they be 475 miles apart?

Solve the problem. -A rectangular Persian carpet has a perimeter of 248 inches. The length of the carpet is 28 inches more than the width. What are the dimensions of the carpet?

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 10 miles per hour. In how many hours will they be 57 miles apart?

Solve the problem. -Jim had grades of 67 and 88 on two chemistry tests. What is the lowest score he can get on the third test to maintain an average of 75?

Solve the problem. -Janet drove 325 kilometers and the trip took 5 hours. How fast was Janet traveling?