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

PostPosted: Fri Jun 15, 2012 9:32 pm
by nsguy1350
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?

Re: AMC 12A 2012 #5

PostPosted: Sat Jun 16, 2012 11:15 am
by darksaber21
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]