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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Sub 505 (Easy)

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

555-605 (Medium)

Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

655-705 (Hard)

John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

Sub 505 (Easy)

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

555-605 (Medium)

In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?

Sub 505 (Easy)

Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

Sub 505 (Easy)

In a weight-lifting competition, the total weight of Joe's two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?

Sub 505 (Easy)

There are 4 more women than men on Centerville's board of education. If there are 10 members on the board, how many are women?

Sub 505 (Easy)

A project scheduled to be carried out over a single fiscal year has a budget of

12, 600, d i v i d e d in t o 12 e q u a l m o n t h l y a l l oc a t i o n s . A tt h ee n d o f t h e f o u r t hm o n t h o f t ha t f i sc a l y e a r, t h e t o t a l am o u n t a c t u a l l y s p e n t o n t h e p r o j ec tw a s

4,580. By how much was the project over its budget?

505-555 (Easy)

A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he has available to spend will be equal to half the amount that he spends this year?

505-555 (Easy)

Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

Sub 505 (Easy)

The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

Sub 505 (Easy)

A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of

38.00, an d o n T u es d a y t h es t or eso l d 20 ma p s an d 15 b oo k s f or a t o t a l o f

60.00. At this store, how much less does a map sell for than a book?

555-605 (Medium)

According to a car dealer's sales report, 1/3 of the cars sold during a certain period were sedans and 1/5 of the other cars sold were station wagons. If N station wagons were sold during that period, how many sedans, in terms of N, were sold?

555-605 (Medium)

A certain company retirement plan has a "rule of 70" provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?

Sub 505 (Easy)

If stock is sold three months after it is purchased, the formula above relates p, d, s, and r, where p is the purchase price of the stock, d is the amount of any dividend received, s is the selling price of the stock, and r is the yield of the investment as a percent. If Rose purchased

400 w or t h o f s t oc k r ece i v e d a

5 dividend and sold the stock for $420, for three months after purchasing it, what was the yield of her investment, according to the formula? (Assuming she paid no commissions.)

Sub 505 (Easy)

A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of

90 p er u ni t an d a l l o f t h e p r o d u ce d u ni t s a r eso l d e a c hm o n t h . W ha t i s t h e minim u m se l l in g p r i ce p er u ni tt ha tw i l l e n s u r e t ha tt h e m o n t h l y p r o f i t (r e v e n u e f r o m s a l es min u s t h e man u f a c t u r e r^{'} scos tt o p r o d u ce) o n t h es a l eso f t h ese u ni t s w i l l b e a tl e a s t

42,000?

Sub 505 (Easy)

A poll reveals that the average (arithmetic mean) income of 10 households is

25, 000. I f 6 o f t h e h o u se h o l d s ha v e in co m eso f

30,000 each, what is the average income of the other 4 households?

Sub 505 (Easy)

A company accountant estimates that airfares next year for business trips of a thousand miles or less will increase by 20 percent and airfares for all other business trips will increase by 10 percent. This year total airfares for business trips of a thousand miles or less were

9, 900 an d ai r f a r es f or a l l o t h er b u s in ess t r i p s w er e

13,000. According to the accountant's estimate, if the same number of business trips will be made next year as this year, how much will be spent for airfares next year?

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