SOLUTION: Alex, Bernard and Cindy had a total of 840 sweets. The ratio of the number of sweets Bernard had to the number of sweets Cindy had was 1:4. After Alex and Bernard each gave away 1/

Question 1188046: Alex, Bernard and Cindy had a total of 840 sweets. The ratio of the number of sweets Bernard had to the number of sweets Cindy had was 1:4. After Alex and Bernard each gave away 1/2 of their sweets, the 3 children had 620 sweets left. How many sweets did Bernard have at first?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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Alex, Bernard and Cindy had a total of 840 sweets.
The ratio of the number of sweets Bernard had to the number of sweets Cindy had was 1:4.
After Alex and Bernard each gave away 1/2 of their sweets, the 3 children had 620 sweets left.
How many sweets did Bernard have at first?
~~~~~~~~~~~~~~~~~

Let "x" be the number of sweets Bernard had at first.

Then the number of sweets Cindy had initially was 4x;

and the number of sweets Alex had initially was the rest, (840-x-4x) = 840-5x.


After Alex and Bernard each gave away 1/2 of their sweets, the 3 children had 620 sweets left. 


Mathematical translation is THIS equation


    0.5 * ((840-5x) + x) + 4x = 620    for the remaining sweets.


Simplify


    0.5*(840-4x) + 4x = 620

    420 - 2x + 4x     = 620

    420   + 2x        = 620

            2x        = 620 - 420 = 200

             x                    = 200/2 = 100.


ANSWER.  Bernard had 100 sweets at first.

Solved.

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