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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555-605 (Medium)

The price of gasoline at a service station increased from

1.65 p er g a l l o n l a s tw ee k t o

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)

Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

555-605 (Medium)

A service provider charges c dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If x is an integer greater than 50, which of the following expressions gives this service provider's charge, in dollars, for a month in which x hours of service were used?

Sub 505 (Easy)

Based on the rates above, how much would Company X charge a customer with a low-use contract for using 95 message units in a month?

555-605 (Medium)

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid

3.99 f or e a c ha dd i t i o na l co m p a c t d i sc p u r c ha se d . I f a p r e f er r e d c u s t o m er p u r c ha se d a t o t a l o f 6 co m p a c t d i scs an d p ai d

15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

555-605 (Medium)

AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 4:00 P.M. x grams 7:00 P.M. 14.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

Sub 505 (Easy)

Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebeccaâs age is twice her daughterâs age?

555-605 (Medium)

A certain fruit stand sold apples for

0.70 e a c han d banana s f or

0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

Sub 505 (Easy)

A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

505-555 (Easy)

Car X averages 25 miles per gallon of gasoline and Car Y averages 11.9 miles per gallon. If each car is driven 12,000 miles, approximately how many more gallons of gasoline will Car Y use than Car X ?

555-605 (Medium)

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?

Sub 505 (Easy)

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 12 3 8 pounds, and on Tuesday, 4 packages weighing an average of 15 1 4 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

555-605 (Medium)

At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

605-655 (Medium)

The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

Sub 505 (Easy)

The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

Sub 505 (Easy)

A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?

Sub 505 (Easy)

A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

Sub 505 (Easy)

Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

555-605 (Medium)

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by

1, 10 f e w er o f t h e t o w e l sco u l d b e b o ug h t f or

120, excluding sales tax. What is the current price of each towel?

555-605 (Medium)

A dealer originally bought 100 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?

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