ElectricPavlov

For how many years is that interest?

I will assume 1 year

x = 5% amount

8000 - x = 9% amount

.05 x  + .09 (8000-x ) 620

.05x - .09 x + 720 = 620

-.04x = -100

x = $ 2500  in 5% account       the remainder     8000-2500 = $ 5500 = amount in 9% account

original amount of banana chips = 10% x 15 lbs = 1.5 pounds

add x pounds of banana chips......   now you have   1.5 + x  lbs of banana chips in the mix

    the final mix has the same amaount of banana chips

       the final mix is 25% banana chips     the final weight is  15 + x  

            so the final amount of banana chips is  .25(15+x)....

                 and as stated above, this equals     1.5 + x

sooooo   1.5 + x = .25(15+x)       solve this for x......you will find x = 3 lbs

I THINK this is the box part:

old mix      15       10   = 1.5

add bc        3       100 =  3

new mix     18       25   = 4.5

You asked for the solution and you would do the box part....the solution is add 3 lbs of banana chips to the original 15 lb mixture to get 18 pounds of 25% banana chips.....     OK now?  

15 lbs * 10 %  = 1.5 lbs banana

  now add x lbs banana chips

1.5 + x lbs = 25% * (15 lbs + x lbs)

1.5 + x = 3.75 + .25 x     solve for x = 3 lbs banana chips

Correct-a-mundo!

It is WAY easier to solve this NOT using the clumsy box method:

You have two equations:

300 = 2(s+w)     or    150 = s+w      (by dividing both sides of the equation by 2)

270 = 2 (s-w)     or    135 = s-w           <------ Now ADD the two equations together

                                 285 + 2s       thus s = 142.5 = plane speed in still air

I havn't any idea how to make this into a quadratic to solve by the Box method

(this ' box method', I think is crazy....sorry you are being taught this method)...

What box?

The Tan function is flipped around the x axis....so it is one of the   - tan    answers

The graph is shifted to the RIGHT (or it COULD be shifted to the left.....but that is not one of the answers)  

    if shifted to the right then pi/2 is SUBTRACTED

so answer  D

When flying WITH the wind his rate is   s +w        where s = plane speed  w = wind speed

so   d = r * t

       300 = (s+w) * 2

AGAINST the wind, his rate is   s - w

so  270 = (s-w)*2                                       Now you have two equations and two unknowns....solve the system of equations to find ' s '