Word Problems Quiz

1. A bus travels 300 miles on 12 gallons of gasoline. At this rate, how many gallons will it need to travel 650 miles?

25 gallons

26 gallons

5.5 gallons

28 gallons

To find the number of gallons needed to travel 650 miles, we can set up a proportion using the given information. We know that the bus travels 300 miles on 12 gallons of gasoline, so the ratio of miles to gallons is 300/12. We can set this ratio equal to the unknown number of gallons needed to travel 650 miles over 650 miles. Solving for the unknown, we find that the bus will need 26 gallons of gasoline to travel 650 miles.

Explanation

To find the number of gallons needed to travel 650 miles, we can set up a proportion using the given information. We know that the bus travels 300 miles on 12 gallons of gasoline, so the ratio of miles to gallons is 300/12. We can set this ratio equal to the unknown number of gallons needed to travel 650 miles over 650 miles. Solving for the unknown, we find that the bus will need 26 gallons of gasoline to travel 650 miles.

2. Two machines can complete 5 tasks every 4 days. Let t represent the number of tasks these machines can complete in a 31-day month. Which proportion can be used to solve for the value of t?

31/10 = t/4

4/31 = t/5

5/4 = t/31

4/5 = t/31

The proportion that can be used to solve for the value of t is 5/4 = t/31. This proportion is derived from the given information that two machines can complete 5 tasks every 4 days. By setting up a proportion, we can determine how many tasks these machines can complete in a 31-day month (represented by t).

Explanation

The proportion that can be used to solve for the value of t is 5/4 = t/31. This proportion is derived from the given information that two machines can complete 5 tasks every 4 days. By setting up a proportion, we can determine how many tasks these machines can complete in a 31-day month (represented by t).

3. At a concert, people's hands were stamped as they walked in. To estimate the attendance, the staff randomly stamped 120 people's hand with a red stamp instead of a blue stamp. A random sample of 250 people in the crowd found 4 people with a red stamp. What is the best estimate for the size of the crowd?

7500 people

9375 people

5625 people

11,250 people

The best estimate for the size of the crowd is 7500 people. This is determined by taking the ratio of the number of people with a red stamp in the sample (4) to the total number of people stamped with a red stamp (120), and then multiplying it by the total number of people in the crowd (x). This can be expressed as (4/120) * x = 250. Solving for x, we get x = 7500. Therefore, the best estimate for the size of the crowd is 7500 people.

Explanation

The best estimate for the size of the crowd is 7500 people. This is determined by taking the ratio of the number of people with a red stamp in the sample (4) to the total number of people stamped with a red stamp (120), and then multiplying it by the total number of people in the crowd (x). This can be expressed as (4/120) * x = 250. Solving for x, we get x = 7500. Therefore, the best estimate for the size of the crowd is 7500 people.

4. A jumbo je carries 330 passengers, 32 in first class and the remainder in coach. If the average first class ticket is $860 and the average coach ticket is $360, how much money will the airline gross if the plane is full?

$267,800

$201,300

$137,780

$134,800

The total number of passengers on the plane is 330. Since 32 passengers are in first class, the remaining 330 - 32 = 298 passengers are in coach. The average revenue from first class tickets is $860, so the total revenue from first class is 32 * $860 = $27,520. The average revenue from coach tickets is $360, so the total revenue from coach is 298 * $360 = $107,280. Therefore, the total revenue from the plane is $27,520 + $107,280 = $134,800.

Explanation

The total number of passengers on the plane is 330. Since 32 passengers are in first class, the remaining 330 - 32 = 298 passengers are in coach. The average revenue from first class tickets is $860, so the total revenue from first class is 32 * $860 = $27,520. The average revenue from coach tickets is $360, so the total revenue from coach is 298 * $360 = $107,280. Therefore, the total revenue from the plane is $27,520 + $107,280 = $134,800.

5. A nonstop bus ride from the bus stateion in Atlantic City, New Jersey, to the bus station in Albany, New York, took 6 hours. If the average speed of the bus was 21 m/second, what is the distance between the two bus stations, to the nearest kilometer.

756 km

454 km

126 km

350 km

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Explanation

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