Application of Systems of Equations

Could someone please help me with this problem. I'm having a bit of trouble. It would be much appreciated. Thanks.


A dog food manufacturer makes three types of dog food mix. Each type is sold in bags containing 5 kg with the ratio of meat : rice : vegetables being as follows:
Mix A Meaty Lumps 5 : 3 : 2
Mix B Balanced Lumps 1 : 1 : 3
Mix C Vegetarian Lumps 0 : 3 : 2
The manufacturer orders 3350 kg of meat, 4850 kg of vegetables and 4300 kg of rice for a particular run. The run is a simple mix and involves no weight loss for any of the ingredients and all quantities ordered are exactly used up. If the run produces x bags of Mix A, y bags of Mix B and z bags of Mix C write three equations that apply and solve them to find x, y and z.

You sum the proportions of meat in meaty lumps, meat in balanced lumps and meat in vegetarian lumps altogether, equal to 3350 Kg and, then, solve for x. If you do the same for rice and vegetables, you will find y and z. Simple!