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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655-705 (Hard)

Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

705-805 (Hard)

In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?

555-605 (Medium)

To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

505-555 (Easy)

Company Q plans to make a new product next year and sell each unit of this new product at a selling price of

2. T h e v a r iab l ecos t s p er u ni t in e a c h p r o d u c t i o n r u na r ees t ima t e d t o b e 40

5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

505-555 (Easy)

If 65 percent of a certain firmâs employees are full-time and if there are 5,100 more full-time employees than part-time employees, how many employees does the firm have?

Sub 505 (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)

An auction house charges a commission of 15% on the first

50, 000 o f t h es a l e p r i ceo f ani t e m, pl u s 10

50,000. What was the price of a painting for which the house charged a total commission of $24,000?

Sub 505 (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. T h e p e t d e p os i t an dJ o na t han \overset{a}{^}  ss ha r eo f t h e m o n t h l y r e n t f or t h e f i r s t m o n t h t o t a l e d

525. How much is the monthly rent on the apartment?

555-605 (Medium)

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 doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

505-555 (Easy)

Exchange Rates in a Particular Year $1 = 5.3 francs $1 = 1.6 marks An American dealer bought a table in Germany for 480 marks and sold the same table in France for 2,385 francs. What was the dealer's gross profit on the two transactions in dollars?

Sub 505 (Easy)

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?

Sub 505 (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)

Sam has

800 inhi s a cco u n t . H e w i l l d e p os i t

1 in his account one week from now,

2 tw o w ee k s f r o mn o w, an d e a c h w ee k t h er e a f t er h e w i l l d e p os i t anam o u n tt ha t i s

1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

Sub 505 (Easy)

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost

80 e a c h, an d t h ose w or nb y G r o u pB cos t

90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

Sub 505 (Easy)

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

555-605 (Medium)

The graph shows the number of computers assembled during each of 6 consecutive days. From what day to the next day was the percent change in the number of computers assembled the greatest in magnitude ?

Sub 505 (Easy)

ÂA certain method for calculating pediatric drug dosages states that if d is the adult dosage, in milligrams, and y is the childâs age, in years, then the childâs dosage, in milligrams, is d Ã (y + 1 24) . If the adult dosage for a particular drug is 800 milligrams, what is an 8-year-old childâs dosage, in milligrams, according to this method?

Sub 505 (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?

Sub 505 (Easy)

To rent a tractor, it costs a total of x dollars for the first 24 hours, plus y dollars per hour for each hour in excess of 24 hours. Which of the following represents the cost, in dollars, to rent a tractor for 36 hours?

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