F2.Maths(20 points)

1.Let the smaller value be 5n, then the larger value is 5n+5
5n greater (5n+5)/2
10n greater 5n+5
5n greater 5
n great 1
so the least value of n is 2
the least value of two number is 10 and 15


2. Let the no. of questions she has answered correctly be x
then the no. of questions she has answered wrongly is 12-x

2x -(12-x) greater 12
3x -12 greater 12
3x greater 24
x greater 8

so the least number of questions she has answered correctly is 9

Answer: Let n be any number, so that

Since there are two consecutive mulitples of 5,

let the smaller number is 5n
and then next number is 5n+5

and the smaller number is greater than half of the larger one

therefore 5n > (5n+5)/2

10n > 5n + 5
5n > 5
n>1

If the consecutive multiples are integers, then n = 2

The consecutive mutiples are 10 and 15

(Model Answer)

However, if the consecutive mutiples are real numbers, then n = 1.00000000....1

The consecutive mutiples are 5.0000000......5 and 10.00000000.......5

(Funny Answer)

2) Let C be number of correct answers and I be the number of Incorrect Answer

C + I = 12 ( Mandy answered total 12 questions, which is the
Total correct and incorrect answered questions)

I = 12 - C

Total correct answers earned 2 x C = 2C marks
Total Incorrect answers deducted - 1 x I = - I marks
= - (12 - C) marks
= C - 12 marks

If Mandy scored greater than 12 marks

2C + (C - 12) > 12

3C > 24

C > 8

Mandy must correctly answer more than 8 questions

Mandy answered 9 questions corrects AT LEAST.

1. let 5x and 5x+5 be two consecutive multiples of 5, where x is a positive integers.
2(5x) > 5x+5
10x - 5x > 5
5x > 5
x > 1
the least value of x is 2
5(2) and 5(2)+5
therefore, the least values of these two numbers is 10 and 15.

2. let x be each correct answer and x/2 be each incorrect answer, where x is a positive integers.
x + x/2 > 12
3x > 24
x > 8
therefore, she at least answerd 9 question correctly.