ElectricPavlov

20 + 35   +  connie  + ashton  + people between  = 98

people betwen = 41 ppl

Base 3 largest 4 digit number   2222  =  80₁₀

  smallest   base 3 number        1000 =  27₁₀

Largest 2-digit base 6      55  =  35₁₀

  smallest                          10  = 6₁₀

So  the numbers that are 4 digit in base 3   and 2 digit in base 6 go from 27₁₀  thru  35₁₀        I'll let you finsish from here......

You are welcome !

a)  substitute  t = 10 into the equation to find their height at ten seconds

        subtract this height from 5500  to find how far they have falllen

b) sbstitute 1000 for  H    then solve for  t   in the equation

c)  h will = 0 when they smack into the ground if they do not open a chute

           use H = 0     to find the total time to fall from the plane to the ground

               then subtract the answer from b to find how much time is left !

When they meet, they have covered one full lap of the track together

  they meet at 30 seconds, then

  alice takes 20 more seconds  for a total of 50 seconds per lap

  alice has covered 3/5    and  bert has only covered 2/5  of a lap

2/5 x = 30 seconds

x = 75 sec for bert -lap

Here is one way   start at 99 and count backwards by 5's until you hit a multiple of 12

   99 - 5 = 94

         94 - 5 = 89

             89 - 5 = 84    Bingo !     84/12 = 7 large boxes     and 3 small boxes

But wait....     what about 24 ?     then there would be 2 large boxes    and  15 small boxes

Find per unit wt of tack

(1590 - 1470) / 40    gm / tack

Now divide starting wt / unit weight to find tacks

1590 gm /  [(1590 - 1470) / 40] gm/tack     = 530 tacks

You can see from the diagram that Henry is 24 ft   east and   32 ft south of his start

   using pythag theorem

      24^2 + 32 ^2 = d ^2

           d = 40 ft from the starting point

First , find out how much money they had to start

a       +      a-48       = 160

2a = 208

a = 104       then t =  56

the t spends some money and this is the result:

(56 - s) *4   =  104

224 - 4s = 104

-4s = -120

s = 30                       t   spent   $ 30 at the store  

a = adult tix                         price total = $ 8a

c = child tix = 50 - a             price total = $ 4 (50-a)           summed , they equal $312

8a      +      4(50-a)          =    312

4a      +       200                = 312

a = 28           then   c = 50 -a = 22