The DryFroot Company makes one pound 16 oz boxes of FrootMix

The DryFroot Company makes one pound (16 oz) boxes of FrootMix. Each box is made to the same recipe and has a positive integral number of ounces of apples, bananas, cranberries and dates. The company also makes one pound boxes of MixedFroot. and although the recipe is different, each box still contains an integral number of ounces of the same four fruits. Finally, DryFroot produces giant boxes of TootyFrooties by mixing four pounds of FrootMix with three pounds of MixedFroot. In each of the three products, the weights of the four fruits are different. The respective boxes list the ingredients in descending order by weight as follows: FrootMix: dates, cranberries, bananas, apples; MixedFroot: apples, bananas, cranberries, dates; TootyFrooties: bananas, cranberries, dates, apples. How many ounces of each fruit are there in a box of each product?

Solution

Froot Mix : 1date,3cranberry,5bananas,7apples

Mixed fruit : 1apple,3bananas,5cranberries,7dates

TootyFruity :29bananas,27cranberris,25dates,31apples,