Word Problems

Word problems test translation before they test math: rates and work, mixtures, overlapping sets, age and interest problems, and weighted averages. The arithmetic inside is rarely hard — the challenge is converting three sentences of story into equations quickly and without inventing constraints the problem never stated. Practice writing the setup in a fixed, boring format every time (define variables, one equation per fact), and learn the standard templates: rate × time = work, the two-set matrix, and the teeter-totter method for weighted averages.

Mixtures, rates, distances, ages.·Show:20 30 50

All

Start Practice

Sub 505 (Easy)

During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?

Sub 505 (Easy)

In a small snack shop, the average (arithmetic mean) revenue was

400 p er d a y o v er a 10 - d a y p er i o d . D u r in g t hi s p er i o d, i f t h e a v er a g e d ai l y r e v e n u e w a s

360 for the first 6 days, what was the average daily revenue for the last 4 days?

Sub 505 (Easy)

The total cost for Company X to produce a batch of tools is

10, 000 pl u s

3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company Xâs gross profit per tool is

Sub 505 (Easy)

If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

605-655 (Medium)

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

705-805 (Hard)

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

Sub 505 (Easy)

A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?

605-655 (Medium)

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

Sub 505 (Easy)

Abdul, Barb, and Carlos all live on the same straight road, on which their school is also located. The school is halfway between Abdulâs house and Barbâs house. Barbâs house is halfway between the school and Carlosâs house. If the school is 4 miles from Carlosâs house, how many miles is Abdulâs house from Carlosâs house?

Sub 505 (Easy)

While a family was away on vacation, they paid a neighborhood boy

11 p er w ee k t o m o w t h e i r l a w nan d

4 per day to feed and walk their dog. If the family was away for exactly 3 weeks, how much did they pay the boy for his services?

Sub 505 (Easy)

Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was $40, what was the total price of all 11 doors?

505-555 (Easy)

A bicycle store purchased two bicycles, one for

250 an d t h eo t h er f or

375, and sold both bicycles at a total gross profit of

250. I f t h es t or eso l d o n eo f t h e bi cy c l es f or

450, which of the following could be the store's gross profit from the sale of the other bicycle?

555-605 (Medium)

Greg assembles units of a certain product at a factory. Each day he is paid

2.00 p er u ni t f or t h e f i r s t 40 u ni t s t ha t h e a sse mb l es an d

2.50 for each additional unit that he assembles that day. If Greg assembled at least 30 units on each of two days and was paid a total of $180.00 for assembling units on the two days, what is the greatest possible number of units that he could have assembled on one of the two days?

Sub 505 (Easy)

A certain restaurant that regularly advertises through the mail has 1,040 cover letters and 3,000 coupons in stock. In its next mailing, each envelope will contain 1 cover letter and 2 coupons. If all of the cover letters in stock are used, how many coupons will remain in stock after this mailing?

505-555 (Easy)

From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000 ?

Sub 505 (Easy)

When traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

Sub 505 (Easy)

A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed?

505-555 (Easy)

A certain store will order 25 crates of apples. The apples will be of three different varietiesâMcIntosh, Rome, and Winesapâand each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?

605-655 (Medium)

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014 ?

605-655 (Medium)

The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and reset the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off ?

← PreviousPage 3 of 10Next →