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# Basic Algebra

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25 Algebra problems.
1. Which number is prime?

A) 4 B) 43 C) 39 D) 121

2. Find the GCF for 14 and 21.

A) 1 B) 6 C) 7 D) 42

3. Find the LCM for 13 and 78.

A) 1 B) 13 C) 78 D) 1014

4. Convert to a fraction.

A) B) C) D)

5. Convert 0.4 to a fraction and write the result in lowest terms.

A) B) C) D)

6. Multiply. 5.34 ? 3.17

A) 15.9378 B) 16.6478 C) 15.6478 D) 16.9278

7. Write the following phrase using symbols. " The quotient of p minus q, divided by 5"

A) B) C) D)

8. Which of the following is not an expression?

A) y(z + 10) B) y - ÷ z C) z?y - 8 D) z + y + 4

9. Which property of the real numbers is illustrated by the following statement?
(2 + 16) + 3 = 2 + (16 + 3)

A) Commutative property of addition C) Distributive property
B) Associative property of addition D) Identity Property

10. Find the median.
13, 17, 40, 46, 54, 26, 52, 31

A) 35.5 B) 13 C) 31 D) 40

11. Evaluate. 8 + 2 ? 5 - 24 ÷ 6 ? 2

A) 16 B) 10 C) 48 D) 42

12. Evaluate if m = -2, n = 4, and p = -1.

A) -24 B) 24 C) -16 D) 16

13. Solve. 2x + 4 = -8

A) -8 B) 0 C) -6 D) -2

14. Solve. - 6 = 12

A) 36 B) C) D) 45

15. Tickets for a play at the community theater cost \$16 for an adult and \$10 for a child. If 270 tickets were sold and the total receipts were \$3420, how many of each type of ticket were sold?

A) 100 adult tickets, 120 child tickets B) 140 adult tickets, 200 child tickets
C) 80 adult tickets, 110 child tickets D) 120 adult tickets, 150 child tickets.

16. A furniture store marks up items 20% (based on cost). If the furniture store buys a couch for \$350, what will the selling price be?

A) \$410 B) \$420 C) \$430 D) \$440

17. A bracelet was marked up \$175 from cost, which amounts to a 50% increase. Find the original cost of the bracelet.

A) \$365 B) \$360 C) \$360 D) \$350

18. Solve and graph the solution set. 3x &#8805; 7x + 20

A)
-5 0
B)
-5 0
C)
0 5
D)
0 5

19. Give the coordinates of the point graphed below.

A) (0, 4) B) (4, 0) C) (0, -4) D) (-4, 0)

20. Find the slope of the line passing through the points (-5, 5) and (-3, 5).

A) 0 B) 1 C) 2 D) Undefined

21. Use the following tabe to answer the question.
Population of Europe by Age Groups
Population (in thousands)
1950 1970 1995
Age 0-14 143,175 166,367 139,464
Age 15-64 359,162 421,432 487,110
Age 65+ 44,981 68,642 101,338
Age 75+ 14,553 22,762 38,139
Total 547,318 656,441 727,912
Source: European Rural Development (ERD) Project.

What percentage of Europe's population was in the age 75+ group in 1970?

: A) 6.0% B) 4.5% C) 5.0% D) 3.5%

22. Write the equation of the line with slope -5 and y-intercept (0, 5).

A) y = 5x - 5 B) 5x - 5y = 0 C) y = -5x + 5 D) -5y = 5

23. Match the graph with one of the equations.

A) B) C) y = 2x - 1 D)

24. Determine which two equations represent parallel lines.
(a) y = -5x + 2 (b) y = 5x + 2 (c) y = x + 2
(d) y = -5x + 5

A) (a) and (b) B) (b) and (c) C) (a) and (c) D) (a) and (d)

25. Solve the system by addition.
-4x - 7y = -11
x - 2y = -1

A) (3, -2) B) (-1, 1) C) (3, 2) D) (1, 1)

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## 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.

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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