SOLUTION: Ronald Reagan Rewind As you may know, former President Reagan really enjoyed jelly beans, actually having a jar of them in the Oval Office. Let us say that one day the Chief of S

Question 850132: Ronald Reagan Rewind
As you may know, former President Reagan really enjoyed jelly beans, actually having a jar of them in the Oval Office. Let us say that one day the Chief of Staff posed a mathematical question to the President about the yellow and red jelly beans in that jar. �Sir, if you were to eat 1 red jelly bean, 1/7 of the remaining candies would be red. If instead you were to eat 5 yellow jelly beans, 1/6 of the remaining candies would be red.�
Please determine* how many red jelly beans and how many yellow jelly beans are in the jar.
*Guess and check approaches are not allowable. You must establish a system of equations that describes the scenario and then solve that system for the number of red and yellow jelly beans.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of red jelly beans
Let = number of yellow jelly beans
-------------------------------------
If he eats 1 red, there are remaining
(1)
If he eats 6 yellow, there are remaining
(2)
----------------------------
(1)
(1)
(1)
and
(2)
(2)
(2)
-------------------
Add (1) and (2)
(1)
(2)

and
(2)
(2)
(2)
(2)
There are 11 red and 60 yellow
check:
If he eats 1 red, there are
70 remaining jelly beans
1/7 of 70 is 10 and there are 10 red remaining -OK
---------------------------------------------
If he eats 5 yellow, there are 66 remaining jelly beans
1/6 of 66 is 11, and that is the number of
red remaining -OK

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