SOLUTION: 1512 guavas were placed in three containers, X, Y and Z, at a supermarket. The number of guavas in Container X is 2/7 of the total number of guavas. 190 guavas from Container Y a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1512 guavas were placed in three containers, X, Y and Z, at a supermarket. The number of guavas in Container X is 2/7 of the total number of guavas. 190 guavas from Container Y a      Log On


   



Question 1205383: 1512 guavas were placed in three containers, X, Y and Z, at a supermarket.
The number of guavas in Container X is 2/7 of the total number of guavas.
190 guavas from Container Y and 1/4 of the guavas in Container Z were sold.
The number of guavas left in Container Y was twice the number of guavas left in Container Z. How many guavas were there in Container Y at first?

Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
1512 guavas were placed in three containers, X, Y and Z, at a supermarket.
The number of guavas in Container X is 2/7 of the total number of guavas.
190 guavas from Container Y and 1/4 of the guavas in Container Z were sold.
The number of guavas left in Container Y was twice the number of guavas left in Container Z.
How many guavas were there in Container Y at first?
~~~~~~~~~~~~~~~~~~~~

From the condition, the number of guavas in both containers Y and Z altogether 

was  5/7 of 1512, or  %285%2F7%29%2A1512 = 1080 originally.


Let y be the number of guavas in container Y originally (the value under
the problem's question).  Then the number of guavas in container Y left is (y-190);
the number of guavas in container Z left is  %283%2F4%29%2A%281080-y%29.


So, we can write this equation

    y - 190 = 2%2A%283%2F4%29%2A%281080-y%29.


Simplify and find y

    y - 190 = %283%2F2%29%2A%281080-y%29

    2(y-190) = 3*(1080-y)

     2y - 380 = 3*1080 - 3y

     2y + 3y = 3240 + 380

        5y   = 3620

         y   = 3620/5 = 724.


ANSWER.  The number under the problem's question is 724.

Solved.



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
CONTAINER      startQuantity       aftersomesellQuantity
    X          (2/7)1512            (2/7)1512
    Y              y                 y-190=2(3/4)z
    Z              z                 (3/4)z
TOTAL           1512

system%28432%2By%2Bz=1512%2Cy-190=2%283%2F4%29z%29

system%28y%2Bz=1080%2Cy-190=%283%2F2%29z%29

system%28y%2Bz=1080%2C2y-3z=380%29

E1-E2:

system%28z=356%2Cand%2Chighlight%28y=724%29%29

check:
432%2B724%2B356=1512+
okay