Please help me with these math questions (part 1):?

Question

I want the solutions and answers for these fraction problems. Thank you.

1) Which three figures multiplied by 5 will produce the answer 6?

2) Certainly, you will agree that:
12 eggs = 1 dozen (1)
so, 24 eggs = 2 dozen (2)
also, 6 eggs = 1/2 dozen (3)
so, let's multiply (2) x (3)
144 eggs = 1 dozen
or 12 dozen = 1 dozen
What's wrong with this reasoning?

3) Today, John Century and his three sons are all together 100 years old. Moreover, John is twice as old as his eldest son, who, in turn, is twice as old as the second son, who, it just happens, is twice as old as the youngest son. How old is each of these men?

4) Find the ultimate value of 1 + 1/2 + 1/4 + 1/8 + ...

5) A rabbit is 10m in front of a dog. The dog can run 10m while the rabbit runs 1m. Prove that the dog will never catch the rabbit.

Answer 1

1) 1.2, 1 and 1/5, 6/5

2)You can't multiply units of eggs. You'll get 144 eggs squared and 1 dozen squared. Take the square root of 144 eggs squared and you get 12 eggs. Take the square root of 1 dozen squared and you'll get 1 dozen. 12 eggs = 1 dozen.

3)John is 53 years and 4 months old. The eldest is 26 years and 8 months old. The middle is 13 years and 4 months old and the youngest is 6 years and 8 months old.

4)2

5)You didn't specify if its 10 m/time for the dog and 1 m/time for the rabbit. There's no velocity. So if the dog just runs 10 meters and the rabbit runs 1 meter, the dog doesn't catch up because the rabbit is still a meter ahead. If you meant it to be a velocity then they could be running in different directions since you never specified that the dog was running after the rabbit.

Answer 2

2) 144 is a dozen dozen. (Like 2x * x/2 = x^2)


3) John's age is j, he has 3 sons whose ages are j/2,j/4 and j/8. add their ages and you'll get 100=(1+1/2+1/4+1/8)j = (8+4+2+1)j/8 = 15j/8

j = 800/15 = 53 + 1/3.
The younges't son is eighth of this number, i.e. 6 + 2/3.

4. s = 1+1/2+1/4+1/8+... = 1 + (1 + 2 + 4 + 8 + ... )/2 = 1 + s/2

Subtract s/2 from both sides of s = 1 + s/2 and you'll get

s/2 = 1
or s = 2.

5) You know that as the dog gets nearer to the rabbit, the rabbit advances, so the dog can never get it.

Answer 3

2) what's 24 eggs multiplied by 6 'eggs'? how many bananas will u
get when u add 6 apples to 3 pineapples? if u talk in units, then
ofcourse 144 Sq.eggs is equal to 1 Sq. dozen eggs, but the
absurdity lies in the term 'Square eggs'
3) 6yrs 8 months, 13yrs 4 months, 26 yrs 8 months, 53 yrs 4
months
4) 2
5) in practice the dog will, this one's similar to (4)