SOLUTION: Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups

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Question 369491: Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether.
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
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Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether.
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Equations:
b + r = 280
(2/3)b = (1/2)r
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Rearrange the 1st:
r = 280 - b
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Substitute for "r" and solve for "b":
(2/3)b = (1/2)(280-b)
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(2/3)b = 140- (1/2)b
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[(2/3)+(1/2)]b = 140
(4+3)/6)b = 140
(1/6)b = 20
b = 120 (original # of blue)
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Since r = 280-b = 160 (original # of red)
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Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Let b represent the number of blue cups and r the number of red cups originally purchased

amount of each left is equal according to the question

2/3 * b = 1/2* r  

4/3 *b = r

b + r = 280

b + (4/3)b = 280

(7/3)b = 280

b = 280*(3/7)

b = 120, the original amt of blue cups purchased.  Red = 160 (280-120)

How many used?

1/3*120 + 1/2*140 = 40 + 70 = 100