Page 120 - Algebra

7.
Let the number of questions in the exam be x
No. of questions attempted by Babis = 0.80x
No. of correct questions = 0.60 × 0.80x = 0.48x
No. of incorrect questions = 0.40 × 0.80x = 0.32x
0.48x × 4 + 0.32x × (–1) = 320
1.92x
1.6x = 320 x = 200
8.
= 2𝑥+7 2𝑥− 1
9.
4𝑥2 –49
– 0.32x = 320
4𝑥2−16𝑥+7
(2𝑥)2 –72
=
4𝑥2− 14𝑥−2𝑥 + 7
=
(2𝑥 –7)(2𝑥+7)
2𝑥(2𝑥− 7)−1(2𝑥− 7)
= (2𝑥 –7)(2𝑥+7) (2𝑥− 7)(2𝑥− 1)
Let the numerator be x
The denominator is 12 – x
The fraction becomes 𝑥 12−𝑥
On adding 3 to the numerator and subtracting 5 from the denominator
𝑥+3 =4 12−𝑥−6 5
5(x + 3) = 4(6– x)
5x + 15 =24 – 4x
5x + 4x = 24– 15
9x = 9 x= 1
10.
Fraction = 𝑥 = 1 12−𝑥 11
or even from the answers you can deduce 1 because when you add 3 to the numerator and 11
subtract 6 from the denominator you get 4 5
Let the age of Julie at 14 years be x
Age of the grandmother 14 years ago = 10x
Present age of Julie = x + 14
Present age of the grandmother = 10x + 14
Age of Julie 6 years from now = x + 14 + 6 = x + 20
Age of the grandmother 6 years from now = 10x + 14 + 6 = 10x + 20
As per the question,
10x + 20 = 4(x + 20)
10x + 20 = 4x + 80
6x = 60
Page 119 of 177
Algebra I & II