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Algebra Word Problems Practice Questions Set 6

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Updated on Sep 26, 2011

Algebra Word Problems

Basic algebra problems ask you to solve equations in which one or more elements are unknown. The unknown quantities are represented by variables, which are letters of the alphabet, such as x or y. The questions in this set of practice problems give you practice in writing algebraic equations and using these expressions to solve problems.

  1. The square of a positive number is 49. What is the number?
    1. –7
    2. 7 or –7
    3. 7
  2. The square of a number added to 25 equals 10 times the number. What is the number?
    1. –5
    2. 10
    3. –10
    4. 5
  3. The sum of the square of a number and 12 times the number is –27. What is the smaller possible value of this number?
    1. –3
    2. –9
    3. 3
    4. 9
  4. The area of a rectangle is 24 square inches. The length of the rectangle is 5 inches more than the width. How many inches is the width?
    1. 4 in
    2. 3 in
    3. 6 in
    4. 8 in
  5. The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m2, what is the height in meters?
    1. 6 m
    2. 9 m
    3. 12 m
    4. 4 m
  6. Patrick has a rectangular patio whose length is 5 m less than the diagonal and a width that is 7 m less than the diagonal. If the area of his patio is 195 m2, what is the length of the diagonal?
    1. 10 m
    2. 8 m
    3. 16 m
    4. 20 m
  7. Samantha owns a rectangular field that has an area of 3,280 square feet. The length of the field is 2 more than twice the width. What is the width of the field?
    1. 40 ft
    2. 82 ft
    3. 41 ft
    4. 84 ft
  8. A garden in the shape of a rectangle is surrounded by a walkway of uniform width. The dimensions of the garden only are 35 by 24. The area of the garden and the walkway together is 1,530 square feet. What is the width of the walkway in feet?
    1. 4 ft
    2. 5 ft
    3. 34.5 ft
    4. 24 ft
  9. A pool is surrounded by a deck that has the same width all the way around. The total area of the deck only is 400 square feet. The dimensions of thepool are 18 feet by 24 feet. How many feet is the width of the deck?
    1. 4 ft
    2. 8 ft
    3. 24 ft
    4. 25 ft
  10. Jessica has a picture in a frame with a total area of 288 in2. The dimension of the picture without the frame is 12 in by 14 in. What is the larger dimension, in inches, of the frame?
    1. 2 in
    2. 14 in
    3. 18 in
    4. 16 in
  11. What is the lesser of two consecutive positive integers whose product is 90?
    1. –9
    2. 9
    3. –10
    4. 10
  12. What is the greater of two consecutive negative integers whose product is 210?
    1. –14
    2. –15
    3. 14
    4. 15
  13. Find the lesser of two consecutive positive even integers whose product is 168.
    1. 12
    2. 14
    3. 10
    4. 16
  14. Find the greater of two consecutive positive odd integers whose product is 143.
    1. 10
    2. 11
    3. 12
    4. 13
  15. The sum of the squares of two consecutive positive odd integers is 74. What is the value of the smaller integer?
    1. 3
    2. 7
    3. 5
    4. 11
  16. If the difference between the squares of two consecutive integers is 15, find the larger integer.
    1. 8
    2. 7
    3. 6
    4. 9
  17. The square of one integer is 55 less than the square of the next consecutive integer. Find the lesser integer.
    1. 23
    2. 24
    3. 27
    4. 28
  18. A 4-inch by 6-inch photograph is going to be enlarged by increasing each side by the same amount. The new area is 168 square inches. How many inches is each dimension increased?
    1. 12
    2. 10
    3. 8
    4. 6
  19. A photographer decides to reduce a picture she took in order to fit it into a certain frame. She needs the picture to be one-third of the area of the original. If the original picture was 4 inches by 6 inches, how many inches is the smaller dimension of the reduced picture if each dimension changes the same amount?
    1. 2
    2. 3
    3. 4
    4. 5
  20. A rectangular garden has a width of 20 feet and a length of 24 feet. If each side of the garden is increased by the same amount, how many feet is the new length if the new area is 141 square feet more than the original?
    1. 23
    2. 24
    3. 26
    4. 27
  21. Ian can remodel a kitchen in 20 hours and Jack can do the same job in 15 hours. If they work together, how many hours will it take them to remodel the kitchen?
    1. 5.6
    2. 8.6
    3. 7.5
    4. 12
  22. Peter can paint a room in an hour and a half and Joe can paint the same room in 2 hours. How many minutes will it take them to paint the room if they do it together? Round answer to nearest minute.
    1. 51
    2. 64
    3. 30
    4. 210
  23. Carla can plant a garden in 3 hours and Charles can plant the same garden in 4.5 hours. If they work together, how many hours will it take them to plant the garden?
    1. 1.5
    2. 2.1
    3. 1.8
    4. 7.5
  24. If Jim and Jerry work together they can finish a job in 4 hours. If working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone?
    1. 16
    2. 5.6
    3. 6.7
    4. 6.0
  25. Bill and Ben can clean the garage together in 6 hours. If it takes Bill 15 hours working alone, how long will it take Ben working alone?
    1. 11 hours
    2. 9 hours
    3. 16 hours
    4. 10 hours
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