Instructor: Dr. R.A.G. Seely
2nd Practice Assignment
Algebra & Functions (Maths 201–016)
Linear Equations
Solve for x or explain why there is no solution.
4
5x
= 3(1 − 56 x)
1. x − 8 = 5
28.
2. 4x = 32
29. − 13 x = 3(1 − 91 x)
3. −4 = x + 11
30.
22
12 x
−
5. 3x − 7 = 28
31.
x
2
x+1
3
6. 10 − x = 20
32. − x+2
8 +
7. −19 = 17 − 4x
33. 6x + 8 = 4[3x − 2 − 2(x + 1)]
8. 1 − x = 1
34.
x+2
5
=
35.
4
3 (x
− 3) = 5( 41 x + 13 )
4. 9 + 2x = 1
9.
3
2x
=9
10. 1 −
x
2
−
4
3
37.
x
2
12. 1 − 7x = 0
38.
2
3x
39.
1
10 (35x
3x
2
=
x
3
x
4
=
−x−3
6
+
2−x
4
x−6
4
36. 2 − (x + 5) = 1 − 4x
= −3
11. 14x + 28 = 0
13. 7 +
= 2( 54 x − 73 )
= 10
= 13 (33 −
9x
2 )
+ 2 = 12 ( 53 − x2 )
+ 100) − 72 (x − 47 ) − 12 = 0
14. x = x + 1
40. 3(7 − 2x + x2 ) = 14 + 3x2 − 8(x − 1)
15. x = 2x
41.
16. 3(x + 1) = 2(x + 1) + 5
17. 4 + (1 − x)(−7) = 2(x + 1) − 5 + 5x
18. 8(1 − 2x) = 4(1 − 4x) + 5
19. 12x + 2 = 4 − 2(1 − 2x) + 8x
20. 3(7 + 5x) = 37 − [5(x + 2) − 11x]
21. −9 + [7(3x + 1) − 11x] = −2(1 − 5x)
22. 6(4x + 8) = 12(x + 4)
23.
x
2
24.
2x
3
+
x
3
=
25. x +
7
6
=5
x
5
= 59 x −
11
18
26. 3x − 2 = −2(2x − 5) + 2
27. − x8 +
x
2
+
x
4
=1
2
3x
−
1
5
= 12 ( 56 − 35 x)
Answers
1. 13
2. 8
32.
2
5
33. −12
3. −15
4. −4
5.
31. −4
35
3
6. −10
34. 38
35. 68
36.
4
3
37.
11
2
7. 9
8. 0
14
38. − 11
9. 6
39. x = any real number
10. 8
40.
1
2
41.
37
58
11. −2
12.
1
7
13. 2
14. No solution.
15. 0
16. 4
17. x = any real number
18. No solution.
19. x = any real number
20.
2
3
21. x = any real number
22. 0
23. 6
24. 0
25. −4
26. 2
27.
8
5
28.
10
11
29. No solution.
30. 5
Markups
SP = C + M
M = MR · C
Discounts
SP = OP − D
D = DR · OP
1. C = $120, M R = 15%. SP =?
11. OP = $210, DR = 20%. SP =?
2. C = $70, SP = $105. M R=?
12. SP = $4.25, OP = $5. DR=?
3. C = $120, SP = $180. M =?
13. SP = $187, OP = $255. D=?
4. I went down to St. Catherine Street the other
day and bought a really fancy t-shirt. It
cost me $200, but I found out later that
the store marks up all their merchandise by
25%. What did the store pay for this fancy
t-shirt?
14. A textbook is on sale for $63 after a discount
of 16%. Find the original price of the textbook.
5. I went to the convenience store and bought
a bag of organic milk. It cost me $7.50, but
I know that the store only paid $6. What is
the store’s markup rate for organic milk?
6. I bought a flat-screen TV from Best Buy for
$1404. I have a buddy who works there, and
he told me that Best Buy marks up all their
TVs by 17%. What is Best Buy’s cost for
the TV that I bought?
7. The convenience store pays $1.80 for my favourite bag of chips and then marks it up
15%. What is the selling price for this bag
of chips?
8. The store where I bought my new shoes marks
up their products by 20% . If I paid $48 for
these shoes, how much did the store pay for
them?
9. I only drink the finest orange juice. A litre
of it costs me $174, but I know that the
juice company pays only $150. What is the
markup rate on this very fine litre of juice?
10. My local pet food store marks up its products by 25%. If I paid $65 for a bag of dog
food, what is the store’s cost?
15. A pair of shoes is on sale for 35% off. If they
usually cost $300, what is the sale price?
16. The Super Awesome Smart Toaster is on sale
at $85 after a 32% discount. What was the
original price of the toaster?
17. The Not Very Awesome Dumb Toaster is on
sale at $133. If the original price is $175,
what is the discount rate on this toaster?
18. I bought a Twilight novel on sale for $9.75.
It was for a friend. Apparently this was 25%
off the original price. What was the original
price?
19. A hat shaped like a wild turkey is on sale
for $126. It’s a very nice looking turkey hat.
If the original price is $152, what is the discount on this item?
20. When I see an Xbox on sale for 12%, I buy
it, even if I already own an Xbox. Last time
I did this it cost me $176. What was the
original price?
21. I bought a smartphone on sale for $99. The
original price was $150. What was the discount rate for this smartphone?
22. An exercise bike is on sale for $390 after a
discount of 25%. Find the regular price of
the bike.
Answers
1. $138
2. 50%
3. $60
4. $160
5. 25%
6. $1200
7. $2.07
8. $40
9. 16%
10. $52
11. $168
12. 15%
13. $68
14. $75
15. $195
16. $125
17. 24%
18. $13
19. $26
20. $200
21. 34%
22. $520