SOLUTION: Ann has a 32 ounce bowl of M&M's on her cofee table. The candies are 50% blue M&M's. She eats some of the M&M's (which are 50% blue), then fills the bowl back to 32 ounces with a p

Question 155910: Ann has a 32 ounce bowl of M&M's on her cofee table. The candies are 50% blue M&M's. She eats some of the M&M's (which are 50% blue), then fills the bowl back to 32 ounces with a package of M&M's that contains 20% blue ones. If the resulting full bowl (32 ounces) contains 40% blue M&M's, how many ounces did she eat?
So far, I know that the original bowl had 16 ounces of blue M&M's (32 oz x 50% = 16 oz). The bag she used to refill with had 6.4 oz (32 oz x 20% = 6.4 oz). The final result was 12.8 ounces of blue M&M's (32 oz x 40% = 12.8) I dont know if that info is relevant to the problem or if I am looking at it all wrong.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Ann has a 32 ounce bowl of M&M's on her cofee table.
The candies are 50% blue M&M's.
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She starts with 32 oz ; 16 oz is blue
She eats x oz. of which half is blue
------------------
She now has 32-x oz ; she has 16-(x/2) blue
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She puts back x oz of which 1/5 is blue
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She now has 32 oz ; she has 16-(x/2) + (1/5)x blue
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EQUATION:
blue - blue + blue = blue
16 - (x/2) + (1/5)x = 0.40*32
16 + (1/5 - 1/2)x = 12.8
(-3/10)x = -3.2
x = 32/3
x = 10 2/3 oz.
She ate 10 2/3 oz
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Cheers,
Stan H.
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