SOLUTION: I am having trouble with this lesson, I've tried this problem and cannot figure it out. If you could please help me understand the process that would be wonderful. A dairy needs

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Question 534553: I am having trouble with this lesson, I've tried this problem and cannot figure it out. If you could please help me understand the process that would be wonderful.
A dairy needs 255 gallons of milk containing 5% butterfat.
How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 255 gallons?
I have a box for each % of butterfat used(____of 5% ____of 1%)



Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!

One kind of Milk
=================
Amount = x gallons
Butterfat = 6% = 6/100 = 0.06

other kind of Milk
==================
Amount = 255-x gallons
Butterfat=1%=1/100=0.01

Mixture Milk
===========
Amount = 255 gallons
Butterfat = 5% = 5/100 = 0.05

(Amount of on kind of milk)*(Buttefat)+ (Amount of other kind of milk)*(Buttefat)=(Amount of Mixture milk)*(Buttefat)
(x)(0.06)+(255-x)(0.01)=255*0.05
0.06x+2.55-0.01x=12.75
0.06x-0.01x=12.75-2.55
0.05x=10.2
0.05x/0.05=10.2/0.05
x=204

One kind of Milk
=================
Amount = x = 204 gallons
Butterfat = 6% = 6/100 = 0.06

other kind of Milk
==================
Amount = 255-204 = 51 gallons
Butterfat=1%=1/100=0.01
Conclusion
==========
204 gallons of Milk containing 6% butterfat and 51 gallons of milk containing 1% butterfat must be used to obtain the desired 255 gallons containing 5% butterfat.