# basic algebra problems

See the attachment for algebra word problems and problems with operations.

1. Porfirio went shopping for some clothes. He bought a shirt for $59.98, a pair shoes for $93.19, a hat for $22.95, a coat for $120.85, and socks for $11.29. Estimate to the nearest dollar the total amount of Porfirio's purchases.

2. Divide: 72/6

3. Do the indicated subtraction. 696 - 311

4. Choose the correct list of the factors of the number 8.

5. A custom order requires grams of material that costs ¢ per gram. Find the total cost of the material.

6. Add. 8/21 + 3/14

8. Find the least common multiple of 3, 6, and 9.

9. If 1 gallon (gal) of water weighs 8.34 pounds (lb), how much does 3.75 gal weigh?

10. Write in decimal form.

11. Carlos works 8.25 hours and receives $102.30 pay. What will he receive at the same rate if he works if he works 14 hours?

12. A computer transmits 11 Web pages in 4 seconds to a Web server. A second computer transmits 33 pages in 8 seconds to the server. Are these two computers transmitting at the same speed?

13. Which pair of fractions is proportional?

14. 1,872 is what percent of 520?

15. Due to dwindling reserves of copper ore, the price of a 100-foot spool of copper wire increased 20% this year to $144. What was the old price (last year's price) for a 100-ft spool of wire?

16. You buy a square lot that is 154 yd on each side. What is its size in acres?

17. Is the following set of numbers a perfect triple? 8, 10, 12

18. Are the following two lines parallel, perpendicular, or neither?

19. Find the mean of the following set of numbers. 13, 15, 18, 18, 18, 19, 22, 26, 28, 33

20. Compute as indicated.

21. Perform the indicated operation. 15/13 * 13/15

22. Add -81 + (-13).

25. Perform the indicated operation. (-4)^3

26. Identify the numerical coefficient of the expression. -7t^2

27. Which of the following are not like terms?

28. Which number shown in parentheses is a solution of the given equation?

29. 375 is what percent of 500?

30. Use your calculator to evaluate the expression if x  1.55, y  2.61, and z  2.24. Round your answer to the nearest tenth.

31. Sasha's score on a math test was 96, and Troy's score was 13 points less than Sasha's. What was Troy's score on the test?

33. Tile for a kitchen counter will cost $8 per square foot to install. If the counter measures 14 ft by 3 ft, what will the tile cost?

34. Find two factors of 35 with a difference of 2.

36. Identify the numerator and denominator of the fraction 3/8

37. Find the greatest common factor of 30, 45, and 50.

38. Find the least common multiple of 2 and 7.

41. For the decimal 2.84905: What is the place value of 4?

42. A stereo receiver selling for $445.50 is discounted (or marked down) to $401.95. What is the savings?

43. Write the following as a common fraction or mixed number. 5.679

47. Identify the base in the following application:

The sales tax rate in a state is 7.5%. If you pay a tax of $17.50 on an item that you purchase, what is its selling price?

49. If $3,000.00 is deposited into an account paying 3% interest compounded annually (at the end of each year), how much money is in the account after 4 years? (Round to the nearest cent.)

51. Complete the statement. 18 kg = ________ g

52. Complete the following statement. 12 ft = ________ in.

53. Complete the statement. (Round to the nearest hundredth.) 2.1 kg = ________ oz

54. Complete the following statement. 20 lb = ________ oz

55. Complete the statement. 461 mm = ________ m

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#### Solution Summary

The solution is comprised of detailed explanations of a set of algebra problems, such as operations of numbers, fractions, conversion of units, LCM, GCF, etc.

The solution of basic algebra problems

Use Equation Editor to write mathematical expressions and equations.

1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = 6,000/(200 - 2x)

a. What is the cost to remove 75% of the pollutant?

b. What is the cost to remove 90% of the pollutant?

c. What is the cost to remove 99% of the pollutant?

d. For what value is this equation undefined?

e. Do the answers to sections a. through d. match your expectations? Explain why or why not.

Busch Enteratinment Corporation. (N.D.). Flamingos. Retrieved from http://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htm

2. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test.

a. Write an expression that gives the total cost to test x animals.

b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal.

c. Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.

d. As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below $3.00? If so, identify a value that supports your answer. If not, explain how you know.

e. How many animals should be tested for the average cost to be $5.00 per animal?

3. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.

a. Write an equation using only one variable that could be used to solve for the constant of variation k.

b. A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve. Find the constant of variation k.

c. If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer.

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