MATH 117
Solutions: QUIZ I
To obtain any credit, you must show your work for each problem! Place a box around each
answer. (Note: Calculators are permitted, but not necessary.)
1. [5 pts]
Multiply and simplify:
(3x – 11) (4x + 9)
Solution: (3x – 11) (4x + 9) = 12x2 – 44x + 27x – 99 = 12x2 – 17x – 99
2. [5 pts]
All electronics at the Betaville Smart Buy are reduced by 29%. Tax is 7.5% of
the selling price. If Albertine pays $99 for an IPad at this store, how much was the list
price of the IPad?
Solution: Let x be the list price (in dollars) of the IPad. Since the list price is
reduced by 29%, Albertine must pay (before tax) 0.71x dollars. Since tax is
7.5% of the selling price, Albertine must pay (1.075)(0.71)x dollars at the
checkout. Thus
(1.075)(0.71)x = 99.
Hence x = 99/ {(1.075)(0.71)} = 129.708. Thus the list price was roughly
$129.70 or $129.71 (depending upon rounding).
3. [5 pts]
Solve for x in the following equation
2(x – (x – 11) ) + 3(5 – x) + 9 = 7
Solution:
2(x – (x – 11) ) + 3(5 – x) + 9 = 7
2(x – x + 11) ) + 3(5 – x) + 9 = 7
2(11) + 15 – 3x + 9 = 7
2
22 + 15 – 3x + 9 = 7
46 – 3x = 7
-3x = 7 – 46
-3x = -39
x = 13
[5 pts]
Albertine will be 44 years old x years from now. Boris is y years older than
Albertine. How old is Boris now?
Solution: Albertine is currently 44 – x years old. Since Boris is y years older,
his age is 44 – x + y years.
4. [extra credit]
Solve for x. (Show each step.)
20 (2 – x) + 3(x – 7) – 2[x + 9 – 3{9 – 4(2 – x)}] = 22
Solution:
20 (2 – x) + 3(x – 7) – 2[x + 9 – 3{9 – 4(2 – x)}] = 22
20 (2 – x) + 3(x – 7) – 2[x + 9 – 3{9 – 8 + 4x}] = 22
20 (2 – x) + 3(x – 7) – 2[x + 9 – 3{1 + 4x}] = 22
20 (2 – x) + 3(x – 7) – 2[x + 9 – 3 – 12x] = 22
20 (2 – x) + 3(x – 7) – 2[6 – 11x] = 22
40 – 20x + 3x – 21 – 12 + 22x = 22
5x + 7 = 22
5x = 15
x=3
Nothing proves more clearly that the mind seeks truth, and nothing reflects more glory upon it, than the delight
it takes, sometimes in spite of itself, in the driest and thorniest researches of algebra.
- Bernard de Fontenelle (1708)