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Question 1132811: Winnie-the-Pooh brought a bunch of balloons. Some were green, and the rest were red. Pooh gave some of the balloons to Eeyore, and the rest he gave to Piglet. Piglet got three more balloons then Eeyore did, and Eeyore got two more red balloons than the number of green balloons Piglet got. How many more red balloons than green balloons did Pooh bring?
Answer by ikleyn(52771) (Show Source):
You can put this solution on YOUR website! .
Let P = # of balloons Piglet got;
E = # of balloons Eyeore got;
PG = # of GREEN balloons Piglet got; and
ER = # of RED balloons Eyeore got.
Do not worry that I introduced 2-letter designations for two amounts; they are not the products; they are single values;
I introduced them INTENTIONALLY for your easier reading and understanding.
Then we have these equations from the condition:
P = E + 3 (1) ("Piglet got three more balloons then Eeyore did")
ER = PG + 2 (2) ("Eeyore got two more red balloons than the number of green balloons Piglet got")
Or, EQUIVALENTLY,
P = E + 3 (1')
PG = ER - 2 (2')
----------------------------------Now subtract equation (2') from equation (1'). You will get
P- PG = E - ER + 5. (3)
But (P - PG) is the number of Piglet's RED balloons (which I will denote as PR from now), while
(E - ER) is the number of Eyeore's GREEN balloons (which I will denote as EG thereafter).
So, you have now
from (2) : ER = PG + 2, (4) ( <<<---=== same as (2) )
from (3) : PR = EG + 5. (5) ( <<<---=== it is (3) in the formula form )
Now add two equations (4) and (5). You will get
ER + PR = PG + EG + 7. (6)
Now notice that (ER + PR) is the total number of RED balloons, while (PG + EG) is the total number of GREEN balloons.
Thus from (6) you get the
ANSWER to the problem's question: Pooh brought 7 more RED balloons than GREEN balloons.
Solved.
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Very nice problem : thanks for posting it ! !
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