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

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505-555 (Easy)

Each week, a clothing salesperson receives a commission equal to

15%

of the first

$500

in sales and

20%

of all additional sales that week. What commission would the salesperson receive on total sales for the week of

$1, 300

505-555 (Easy)

Last year

$48, 000

of a certain store's profit was shared by its 2 owners and their 10 employees. Each of the 2 owners received 3 times as much as each of their 10 employees. How much did each owner receive from the

$48, 000

505-555 (Easy)

On a vacation, Rose exchanged

$500.00

for euros at an exchange rate of

0.80

euro per dollar and spent

\frac{3}{4}

of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of

$1.20

per euro, what was the dollar amount she received?

505-555 (Easy)

Each day Linda spends 6 hours at her dog-walking job, for which she is paid

$15.00

per hour. In addition, Linda spends a total of 1.5 hours each day, for which she is not paid, traveling to and from the job. What is Linda's hourly rate of pay for the total amount of time that she spends each day at her dog-walking job and traveling to and from that job?

505-555 (Easy)

If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter?

505-555 (Easy)

A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of

$2.35

. How many of the coins have a face value of 25 cents?

505-555 (Easy)

A retailer purchased eggs at

$2.80

per dozen and sold the eggs at 3 eggs for

$0.90

. What was the retailer's gross profit from purchasing and selling 5 dozen eggs? (1 dozen eggs = 12 eggs)

505-555 (Easy)

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover nonfiction books does Thabo own?

505-555 (Easy)

A bicycle store purchased two bicycles, one for

$250

and the other for

$375

, and sold both bicycles at a total gross profit of

$250

. If the store sold one of the bicycles for

$450

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

505-555 (Easy)

Makoto, Nishi, and Ozuro were paid a total of

$780

for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

505-555 (Easy)

The regular price per can of a certain brand of soda is

$0.40

. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?

505-555 (Easy)

The price of gasoline at a service station increased from

$1.65

per gallon last week to

$1.82

per gallon this week. Sally paid

$26.40

for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline?

505-555 (Easy)

Harry spent

25%

of his

$2, 200

May take-home pay on rent and

30%

of the remainder on food. How much of his May take-home pay did Harry spend on food?

505-555 (Easy)

City

X

has a population 4 times as great as the population of City

Y

, which has a population twice as great as the population of City

Z

. What is the ratio of the population of City

X

to the population of City

Z

505-555 (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?

505-555 (Easy)

Last week Chris earned

x

dollars per hour for the first 40 hours worked plus 22 dollars per hour for each hour worked beyond 40 hours. If last week Chris earned a total of 816 dollars by working 48 hours, what is the value of

x

505-555 (Easy)

A total of

s

oranges are to be packaged in boxes that will hold

r

oranges each, with no oranges left over. When

n

of these boxes have been completely filled, what is the number of boxes that remain to be filled?

505-555 (Easy)

A bicycle race on a mountain trail began at an elevation 850 meters above Town X. The race course consisted of 5 phases, with the following elevation changes: a descent of 280 meters, an ascent of 350 meters, a descent of 620 meters, an ascent of 100 meters, and a descent of 400 meters. At what elevation, in meters above or below Town X, did the race end?

505-555 (Easy)

Jonathan, Kyle, and Michael agreed to pay equal shares of the monthly rent on an apartment. Because Jonathan has a cat, he paid a 1-time pet deposit of

$250

. The pet deposit and Jonathan's share of the monthly rent for the first month totaled

$525

. How much is the monthly rent on the apartment?

505-555 (Easy)

Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD's vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

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