Download Solve the following word problems using algebra. (Show your work!!!)

Name:_________________________ TECM 1303 Activity 5(Due by Apr. 18)
Dear Instructor or Tutor,
These problems are designed to let my students show me what they have learned and what they
are capable of doing on their own. Please allow them to work the problems on their own! If
you would like to help them with similar problems, here are the related homework problems:
pg. 374:#1-29 odd, 35, 39, 41, pg. 379:#1-19 odd, pg. 384:#1-25 odd, 29, 31, 33, 35, Thanks!
Solve the following equations.(Show your steps!)
1.  2 x  5 x  12   0
2. 5x  x  2  x  3  0
3. 5x2  15x  0
4. 10 x 2  11x  3  0
5. 16 x2  1  0
6. 7 x 2  4 x  1  2 x 2  4 x  5
7. 13x 2  17 x  2  4 x  x  2 
8.  2 x  7  x  5  2
9.  2 x  3 3x  4    3x  4  x  5
10. 27 x3  18 x 2  3x  0
11.  x 2  4  4 x 2  4 x  15   0
12.  x 2  9  6 x 2  7 x  5   0
Solve the following word problems using algebra. (Show your work!!!)
13. Find two consecutive even integers whose product is 24 more than eight times the larger
integer.
14. Find two consecutive odd integers whose product is 4 less than three times the larger
integer.
15. The width of a rectangle is 8 feet less than the length. If the area of the rectangle is 33
square feet, what are the dimensions of the rectangle?
16. The base of a triangle is 7 feet less than three times the height. Find the base and height of
the triangle if its area is 13 square feet.
17. The shorter leg of a right triangle is 11 feet shorter than twice the longer leg. The
hypotenuse is 1 foot longer than the longer leg. Find the lengths of the three sides of the
triangle.
18. The lengths of the three sides of a right triangle are consecutive integers. Find the lengths
of the three sides of the triangle.
19. Tom and Mary have a rectangular swimming pool that is 9 feet wide and 12 feet long. They
are going to build a tile border around the pool of uniform width. They have 162 square feet
of tile and they want to use all of it. How wide should the border be?
9
12
?
?
20. A painting and its frame cover 84 square inches. The frame is 2 inches wide at the top and
bottom and 1 inch wide at the sides. The length of the painting is 3 inches more than the
width. What are the dimensions of the painting?
W 3
?
W
1
2
?
Solve the following equations using the Square Root Method or Completing the Square.
21. x 2  169
22. x 2  121
23. 36 x2  121  0
2
24. 4 x  8  4
25.  2 x  1  0
2 5

26.  5 x   
3 9

27. x 2  6 x  16  0
28. x2  4 x  1  0
29. x 2  4 x  29  0
2
2
30. x 2  x  2  0
32. 2 x 2  10 x  37  0
31. 4 x2  12 x  7  0
Solve the following equations using the quadratic formula.
33. 2 x  11x  5  0
34. x 2  50  15 x  6
2
35. x  2 x  3  7
37. 9 x2  6 x  5  0
36. 2 x2  5x  7  0
Bonus#1: Solve each equation. Shade the answers to reveal the name of a very large number.
1.
2.
3.
4.
5.
6.
7.
8.
x2  4 x  3  0
x 2  3x  2  0
x 2  7 x  12  0
x2  8x  7  0
x 2  11x  30  0
x2  17 x  30  0
x 2  13x  40  0
x 2  10 x  9  0
9.
10.
11.
12.
13.
14.
15.
16.
x 2  20 x  36  0
x2  19 x  60  0
x2  15x  36  0
x2  18x  77  0
x2  17 x  72  0
x 2  95 x  1200  0
x 2  35x  250  0
x2  4  0
17.
18.
19.
20.
21.
22.
23.
24.
x 2  x  20  0
x2  2 x  48  0
x2  10 x  24  0
x2  9 x  22  0
x 2  6 x  16  0
x 2  12 x  45  0
x 2  81  0
x 2  3x  54  0
Bonus #2:
What kind of tree did the algebra teacher try to grow?
Solve the following quadratic equations; match your answer with the lettered answers below,
and write the letter in the corresponding numbered box at the bottom.
1) x 2  2  7
5) x 2  18  17
9) 3x 2  1  11
13) x 2  19  249
2) x 2  1  26
6) x 2  1  7
10) 10  2 x2  2
3) x 2  4  4
7) 2 x 2  4  22
11) 12 x 2  2  7
4)  x 2  27
8) 1  x 2  3
12) 13 x 2  1  2
14) 4 x2  5  4
15) 81  16x 2
16) 9 x 2  5
A. 0
C. 4
E. 2
O. 3
Q. 5
R.  6
7
11
8
15
G. 6
3
S. 
2
4
10
13
12
H. 1
5
T. 
3
5
1
14
13
14
I. 3 3
5
U. 
3
2
16
N. 3 2
9
W. 
4
3
6
9
Bonus#3:
(1 and 2)
(1 and 4)
(2 and 5)
(2 and 6)
(3 and 6)
(5 and 1)
6, -6, 0
-11, -1, 0
3 3
,
2 2
1
 ,2
3
-4, -4
5, -3