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 A fruit salad has blueberries, rasberries, grapes and cherries.  The fruit salad has a total of 280 pieces of fruit.  There are twice as many rasberries as blueberries, three times as many grapes as cherries and four times as many cherries as rasberries.  How many cherries are there in the fruit salad?

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Carol H. | Experienced Mathematics Tutor w/ Master's Degree in MathExperienced Mathematics Tutor w/ Master'...
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Let b = number of blueberries           
Let r = number of raspberries
Let g = number of grapes
Let c = number of cherries
 
(1) b + r + g + c = 280   
(2) r = 2b     Substitute equation 2 into equation 4, which means c = 4(2b) or c = 8b (eq. 5)
(3) g = 3c     Substitute equation 3 into equation 5, which means g = 3(8b) = 24b (eq. 6)
(4) c = 4r                       
 
                                 
Now, substitute equations 2, 5, and 6 into equation 1:
b + 2b + 24b + 8b = 280                       r = 2(8)                    c = 4(16)          g = 3(64)
                      35b = 280                       r = 16 raspberries      c = 64 cherries  g = 192 grapes
                       35      35
                          b = 8 blueberries