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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = number of red jelly beans
Let +y+ = number of yellow jelly beans
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If he eats 1 red, there are +r+-1+%2B+y+ remaining
(1) +%28+1%2F7+%29%2A%28+r+-+1+%2B+y+%29+=+r+-+1+
If he eats 6 yellow, there are +r+%2B+y+-+6+ remaining
(2) +%28+1%2F6+%29%2A%28+r+%2B+y+-5+%29+=+r+
----------------------------
(1) +r+-+1+%2B+y+=+7%2A%28+r+-+1+%29+
(1) +r+-+1+%2B+y+=+7r+-+7+
(1) +6r+-+y+=+6+
and
(2) +r+%2B+y+-+5+=+6r+
(2) +5r+-+y+=+-5+
(2) +-5r+%2B+y+=+5+
-------------------
Add (1) and (2)
(1) +6r+-+y+=+6+
(2) +-5r+%2B+y+=+5+
+r+=+11+
and
(2) +-5r+%2B+y+=+5+
(2) +-5%2A11+%2B+y+=+5+
(2) +-55+%2B+y+=+5+
(2) +y+=+60+
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
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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