Grade 9 Mathematics Term 3 0016

If the quotient of k and 9 is equal to the quotient of 9 and k, determine the value(s) of k.

The sum of two consecutive numbers is 49. Determine the two numbers.

Answer explanation

x + x+1 = 49

2x + 1 = 49

2x = 49 - 1

2x = 48

x = 24

The consecutive numbers are 24 and 25.

Simon and Ryan disagree on the answer to the equation:

x(x-2) = (x-3)(x+4)

Simon says the answer is -12, while Ryan says the answer is 4. Check the answer and determine who is correct.

• Simon

• Ryan

• None

• Both

Peter says that the equation: x2 + 2x = 8 has two possible answers, namely x = 2 and x = -4. Without solving the equation, state whether Peter is correct. Why do you think it is possible to have two answers.

Answer explanation

They are both correct answers. Peter is correct. The equation has two answers because it is quadratic, i.e. it is equation of degree 2 (has x to power 2).

You spent 15 minutes more studying for Mathematics than you did for English in one afternoon (like you should!). The two subjects together took you 2 hours and 45 minutes to study. How long did you spend on Mathematics?

Answer explanation

Mathematics = x

English = x-15

Mathematics + English = x + x - 15

Total Time Spent = 2x - 15

2 hours 45 minutes = 2x - 15

2x = 2hrs 45min + 15min

2x = 3hrs

x = 1hr 30min

Time spent studying mathematics is 1hr 30min.

At a full theatre show, there are twice as many women as men. There are 130 children and the maximum number of seats in the theatre is 526. How many seats were filled by adults?

• 390

• 394

• 396

• 390

Answer explanation

Adults = 526 - 130

Adults = 396

At a full theatre show, there are twice as many women as men. There are 130 children and the maximum number of seats in the theatre is 526. How many of the adults were women?

• 288

• 264

• 164

• 266

Answer explanation

Men = x

Women = 2x

x + 2x = 396

3x = 396

x = 132

2x = 264

Women = 264

• 6

• 5.5

• 6.5

• 5.4

• 18ml

• 15ml

• 24ml

• 21ml