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?

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