Word Problems
1. Before the market opens on Monday, a stock is priced at $25. If its price decreases $4 on Monday,
increased $6 on Tuesday, and then decreases $2 on Wednesday, what is the final price of the stock
on Wednesday?
2. If the sum of a, b, and c is twice the sum of a minus b and a minus c, then a=?
3. The average of 5 numbers is 13. If the average of 4 of these numbers is 10, what is the fifth number?
4. Between 1950 and 1960 the population of Country A increased by 3.5 million people. If the amount
of increase between 1960 and 1970 was 1.75 million more than the increase from 1950-1960, what
was the total amount of increase in population in Country A between 1950 and 1970?
5. A painter charges $12 an hour, while his son charged $6 an hour. If the father and his son worked
the same amount of time together on a job, how many hours did each of them work if the combined
charge for their labor was $108?
6. Gheri is n years old. Carl is 6 years younger than Gheri and 2 years older than Jean. What is the
sum of the ages of all three?
7. During a drought the amount of water in a pond was reduced by a third. If the amount of water in the
pond was 48,000 gallons immediately after the drought, how many thousands of gallons of water
were lost during the drought?
8. There is enough candy in a bag to give 12 pieces of candy to each of 20 children, with no candy left
over. If 5 children do not want any candy, how many pieces of candy can be given to each of the
others?
9. John can shovel a certain driveway in 50 minutes. If Mary can shovel the same driveway in 20
minutes, how long will it take them, to the nearest minute, to shovel the driveway if they work
together?
10. Chris has twice as many baseball cards as Lee. If Chris gives Lee 10 of his baseball cards, he will
have half as many as Lee. How many baseball cards do Chris and Lee have together?
11. In a group of 60 workers, the average (arithmetic mean) salary is $80 a day per worker. If some of
the workers earn $75 a day and all the rest earn $100 a day, how many workers earn $75 a day?
1. 25 – 4 + 6 – 2 = 25
2. 2. a + b + c is twice (a – b) + (a – c)
1/2 (a + b + c) = (a – b) + (a – c)
or
1/2a + 1/2b + 1/2c = 2a – b – c
–1.5a = -1.5b – 1.5c
a=b+c
a + b + c = 2[(a – b) + (a – c)]
a + b + c = 4a – 2b – 2c
-3a = -3b – 3c
a=b+c
3. 5 (13) = 65 = sum of five numbers
4 (10 = 40 = sum of four numbers
65 – 40 = 25
4. Increase (1950-1970) = increase (1950-1960) + increase (1960-1970)
Increase (1950-1970) = 3.5 million + (3.5 million + 1.75 million)
Increase = 8.75 million
5. X = hours
12x + 6x = 108
18x = 108
x=6
6. Gheri = n; Carl = n - 6; Jean = (n – 6) – 2
n + n – 6 + n – 6 – 2 = 3n – 14
7. X = total gallons in pool
2/3x = 48,000
x = 72,000
72,000 – 48,000 = 24,000
8. Total candy: 12(20) = 240 pieces
Candy per child in smaller group: 240/15 = 16
9. Rate x Time = Work done
John’s work rate: 1 driveway/50 minutes; Mary’s work rate: 1 driveway/20 minutes
Time = x (for both because they spend equal amounts of time on the driveway)
Work done = 1 driveway
1 driveway (x minutes) + 1 driveway (x minutes) = 1 driveway
50 minutes
20 minutes
x/50 + x/20 = 1
7/100 (x) = 1
x = 100/7 = 14 minutes
10. C = # of Chris’s baseball cards; L = # of Lee’s baseball cards
C = 2L
2(C – 10) = (L + 10)
2(2L – 10) = (L + 10)
4L – 20 = L + 10
3L = 30
L = 10
C = 2L
C = 2 (20)
C = 20
C + L = 10 + 20 = 30
11. Total salary paid = 60 ($80) = $4800
x = number of workers earning $75 per day; (60 – x) = number of workers earning $100 per day
75x + 100(60 – x) = 4800
75x + 6000 – 100x = 4800
–25x = -1200
x = 48