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forum.virtualchallengemeets.com • View topic - AMC 12A 2012 #5

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AMC 12A 2012 #5

American Mathematics Contest & American Invitational Mathematics Examination. See for more information
Note:USAMO/IMO-level questions need to go in the Olympiad section.
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AMC 12A 2012 #5

Postby nsguy1350 » Fri Jun 15, 2012 9:32 pm

A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
2013 District 1/Region:
NS - 319/355
MA - 340/332
CA - 294/287
SC - 344/292
CS - 212/124 (fail)
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Re: AMC 12A 2012 #5

Postby darksaber21 » Sat Jun 16, 2012 11:15 am

Okay, here's my attempt at this problem. I'm first going to set a system of equations:
[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Where:
w = number of blueberries
x = number of raspberries
y = number of grapes and
z = number of cherries

I went ahead and solved the first three equations for z (cherries), so I can plug them in and solve for z:

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]
Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
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