ElectricPavlov

Alex needs 10 quarts of 50%      ....so he needs  5 quarts of antifreeze  and 5 qts water

he currently has only   4 quarts antifreeze   and 6 quarts of water

....a 40% solution

.40 (x)   +   1 (10-x)   =  .50 (10)

.40x + 10 -x = 5

-.6x = -5

x = 5/.6 = 8.333 quarts  of   40%    will be needed to start    then 1.67 quarts of pure antifreeze will be added

10 - 8.33 = 1.67 quarts to drain and refill with 100% a-freeze

80/l   * x      +      125/l * ( 20-x)  = 109 (20)

80x  + 2500- 125x = 2180

- 45x = -320

x = apple juice liters = 7.11        cranberry = 12.89 liters

Yah...I saw Chris answer ..... you posted your equation incorrectly...and I guessed at what it was SUPPOSED to be incorrectly...

   it SHOULD have been

4217 = 600 [ (1+i)^6 -1 ] / i           PARENTHESES AND BRACKETS ARE VERY IMPORTANT IN MATH !!!      

First one:  This descrbes a right triangle with legs 12  and 16      the direct path back to port is the hypotenuse

   Use pythagorean theorem to calculate the hypotenuse

Second one is pythgorean theorem too

     one leg is 9      you are looking ofr the other   and the hypotenuse is 15  

        9^2 + x^2 = 15^2      solve for x

4217 = 600 (1+i)6   - 1/i        Divide through by 600

7.02833 = (1+i)^6  - 1/i

I am not sure how to complete this except graphically......where I get   i = .449     or  44.9 %  

Here is a desmos graph:

https://www.desmos.com/calculator/yb8xvzkdtr

Please proofread your post.....

I think it is supposed to be 4217 = 600 (1+i)⁶   - 1/i    ??

NOT allowed would be   023   (not allowed bcause all 3 positions are the same as yours)  

               also not allowed: 032   203   320   as only two numbers have switched places

ALSO  NOT allowed would be   x23  (nine codes ...we already counted the o23)     0x3   (nine codes....we counted 023)   and  02x    (nine codes again) codes)

total codes POSSIBE    10 x 10 x 10 = 1000

   minus the not allowed codes above = 1000 -1-1-1-1-9-9-9 =___________ possible codes    (I think!)

Great minds think alike......    and ours do too!     Glad we at least arrived at the same answer....it might be correct .      LOL      ~EP

First....graph the given info (see diagram below)

then you will see a triangle   with 'base' of  20    and 'height'     of  4  

    can you compute the area of a triangle   ( 1/2 b h ) ?

You will have 2/3 left

2/3  * 99999 = 66,666