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ELEMENTARY ALGEBRA PRACTICE TEST
CHAPTERS 3 - 4
Solve the proportions for the given variables:
108
9

1.
c
16
2.
2m
7m  1
 7

20
40
Answer _______________________
Answer _______________________
*Solve the following word problems by first defining your variable(s), setting up the equation and then solving.*
3. One mile is approximately equal to 1.6 kilometers. If a runner participates in a 10-kilometer race, how many
miles does she run?
Answer _______________________
4.
The sales tax on a car that sold for $15,000 is $330 more than the sales tax on a car that sold for $11,000.
Find the sales tax on the car that sold for $11,000?
Answer _______________________
5.
The length of a rectangle is seven less than twice the width. If the perimeter is 64 meters, find the width and
the length.
Answer _______________________
6.
A suit normally selling for $220 is reduced by $44. What is the discount as a percent?
Answer _______________________
7.
A bank loaned out $250,000, part of it at the rate of 8% annual mortgage interest and the rest at a rate of 18%
annual credit card interest. The interest received on both loans totaled $23,000. How much was loaned at
each rate?
Answer _______________________
8.
You invest $7200 in two accounts paying 8% and 10% annual interest, respectively. At the end of the year,
the accounts earn the same interest. How much was invested at each rate?
Answer _______________________
9.
Things did not go quite as planned. You invested part of $8000 in a stock that paid 12% annual interest.
However, the rest of the money suffered a 5% loss. If the total annual income from both investments was
$620, how much was invested at each rate?
Answer _______________________
10. Two runners leave SMC, Laura going north and Joseph going south. At the end of 5 hours, they are 40 miles
apart. If Joseph is running 2 miles per hour faster than Laura, find the rate of each runner.
Answer _______________________
11. Patricia is making a floor plan for a house. She wants the length of one bedroom to be two feet more than the
width. If the perimeter is to be 68 feet, find the length and the width of the bedroom.
Answer _______________________
12. Carl has four times as much money invested at 6% annual simple interest as he has at 4% annual simple
interest. If his yearly income from these investments is $560, how much was invested at each rate?
Answer _______________________
13. The sum of two numbers is 100. Their difference is 53. Find the two numbers.
Answer _______________________
14. The difference between two numbers is 12. If the larger number is eight less than three times the smaller, find
the numbers.
Answer _______________________
15. A laboratory technician has one batch of solution that is 35% acid and another batch of solution that is 10%
acid. If she wishes to make 30 liters of a solution that is 25% acid, how much of each will she need?
Answer _______________________
16. When 7 is subtracted from five times a number, the result is greater than twice the sum of the number and 4.
Find all numbers that satisfy the inequality.
Answer _______________________
17. The candy shop makes a 2-pound box of candy that is a mixture of caramels and creams and sells for $4.95
per pound. The caramels sell for $4.50 per pound. The creams sell for $5.10 per pound. How many pounds
of caramels and creams are in the box?
Answer _______________________
18. A car traveled at an average rate of 40 miles per hour and then reduced its average rate to 30 miles per hour
for the rest of the trip. If the 180-mile trip took 5 hours, determine how long the car traveled at each rate.
Answer _______________________
19. Two cities are 315 miles apart. A car leaves one of the cities traveling toward the second city at 50 miles per
hour. At the same time, a bus leaves the second city bound for the first city at 55 miles per hour. How long
will it take for them to meet?
Answer _______________________
20. The amount of material needed to make 15 dresses is 18 yards more than the amount needed for 9 dresses.
How many yards of material is needed to make 9 dresses?
Answer _______________________
21. A rectangular swimming pool has a width of 35 feet and an area of 2450 square feet. What is the pool’s
length?
Answer _______________________
22. A triangle has a base of 5 feet and an area of 20 square feet. Find the height of the triangle.
Answer _______________________
23. A cylinder whose radius is 2 inches and whose height is 3 inches has its radius tripled. How many times
greater is the volume of the larger cylinder than the smaller cylinder? Answer _______________________
24. One angle of a triangle is three times as large as another. The measure of the third angle is 40  more than
that of the smallest angle. Find the measure of each angle.
Answer _______________________
25. The angle=s measure is 78  less than that of its complement. What is the measure of the angle?
Answer _______________________
26. The measure of the angle’s supplement is 51  more than twice the angle. What is the measure of the
angle?
Answer _______________________
Answer _______________________
27. Which one of the following is the better buy: a large pizza with a 16-inch diameter for $12.00 or two small
pizzas each with a 10-inch diameter, for $12.00?
Answer _______________________
28. For the equation y = - x - 4, fill in the missing values in the table of values.
Answer _______________________
x
y
-8
3
-1
29. Is point (- 2, 24) on the graph of y = -7x + 12?
Answer _______________________
30. The point (5, -2) is located in what quadrant?
Answer _______________________
What are the coordinates of the x- and y-intercepts on the graphs of the following lines:
31. -27x + 9y = 54?
X-intercept at __________________
Y-intercept at__________________
32. x = - 4
What is the slope of this line?
Answer--Intercept_____________________
--Slope________________________
33. y = - 6
What is the slope of this line?
Answer--Intercept_____________________
--Slope________________________
34. Rewrite -15x - 45y = -135 in slope-intercept form and identify the slope and the coordinate of the
y-intercept.
slope _______________________
Y-intercept at_________________
35. Find the slope of the line: 3x + 9y = 8.
Answer _______________________
36. Find the slope of the line that goes through the points (- 5, 3) and ( 1, 0).
Answer _______________________
37. Graph y 
2
x  3 by finding the y-intercept and then using the slope to determine a second point on the
5
line.
Y
X
38. Write the equation of the line in all three forms that has a slope of
39.
2
and contains the point (8, -5).
3
Answer _______________________
Write as a linear inequality in two variable:
The sum of three times the x-variable and two times the y-variable is at most 12.
Answer _______________________
40. Find the equation of the line that is parallel to the line 4x = 3y - 10 and contains the point (-2, 2). Write
the equation in slope-intercept form and general form.
Answer _______________________
41. Find the equation of the line that is perpendicular to the line 8x - 5y = 17 and contains the point (- 6, 4).
Write your equation in slope-intercept form and general form.
Answer _______________________
Graph the following on a set of coordinate axes and label the points and line:
42. Graph - 6x + 16y < - 48.
Y
X
43. Graph - 9x - 36y > - 72.
Y
X
44. Graph x > 3.
Y
X
45. Graph 7x + 3y = 15.
Y
X
46.
Graph y < 4.
ANSWERS
1. 192
2. 5
3. 6.25 miles
4. $907.50
5. w= 13”, l = 19”
6. 20%
7. mort.= $220,000, cr.cd.= $30,000
8. 8%--$4,000, 10%--$3,200
9. 12%--$6,000, 5%--$2,000
10. Laura-3mph, Joseph-5mph
11. w= 16’, l = 18’
12. 4%--$2,000, 6%--$8,000
13. 47/2, 153/2
14. 10, 22
15. 35%--18 l., 10%--12 l.
16. x > 5
17. caramels 0.5 lbs., creams 1.5lbs.
18. 40 mph—3 hr, 30 mph—2 hr.
19. 3hours
20. 27yards
21. 70’
22. h = 8’
23. 9 times
24. 28◦, 84◦, 68◦
25. 6◦
26. 43◦
27. large pizza
28. (-8, 4), (-7, 3), (-1, -3)
29. No
30. IV
31. x-interc. (-2, 0), y-interc. (0,6)
32. x-interc. (-4, 0), m = undefined
33. y-interc. (0, -6), m = 0
34. m = -1/3, y-interc. (0, 3)
35. m = -1/3
36. m = -1/2
37. graph
38. S-I: y = - (2/3)x + 1/3, Gen. 2x +3y = 1
39. 3x + 2y < 12
40. S-I: y = (4/3)x +14/3, Gen. 4x – 3y = -14
41. S-I: y = (-5/8)x +1/4, Gen. 5x + 8y = 2
42. graph
43. graph
44. graph
45. graph
46. graph