Brain Busters

Heyy pleasee..I need your help, guys!

help me solve the following probs:

1.)If you multiply my age by 6 and subtract 6 the result is the same as if you subtract 7 from my age and then multiply by 7. How old am I?

2.)The water hyacinth is a fast-growing weed, with a doubling time of only two weeks. A square meter colony of hyacinth is in a lake that is 1 square-kilometer in size. How long would it take to cover the entire lake with water hyacinth?

3.)One bag of potatoes weight 30 kg plus 1/4 of its weight. Another bag weights 32 kg plus 1/5 of its weight. Which bag is heavier?

4.)a number's digital root is a single-digit result of repeatedly adding its digits. For example, the digital root of 6788 is 2, since 6+7+8+8=29 and 2+9=11 and 1+1=2. What is the digital root of the 180-digit number 10111213141596979899, made up of the numbers from 10 tp 99?

Thanks guyss! I'll be waiting :D

4.9?

3.2nd bag

1.43

2.b/w 9 to 10 weeks

edit:

didnt see that this was answered already

1.let your age be x

6x - 6 = 7(x-7)

        =7x - 49

=> x=49-4=43

2.Let the area of the lake occupied by the hyacinth at any time t be A(t)

 Given A(0)=1m^2

A(t)=2*A(t-1)

     =2*2*A(t-2)

    =2*2*2*A(t-3){see the correlation b/w no of 2's and substrant in the bracket}

    =2^t A(t-t)=(2^t)*A(0)

A(t)=1000*1000m^2

=>t=6log10base2

t=2n where n is the no of weeks

which must give the answer

3. bag1=30+30/4=37.5

 bag2 = 32+32/5=38.4

bag 2 is the answer

4.10+11+...+99 is an

   10+99=109

   11+98=109

    12+97=109 and so on 40 times(there are 100 digits)

    Therefore sum is 109*40=4360

   So answer is 4..

lol, man you're out of this world

*subscribes*