SOLUTION: How many gallons of cream that is 20% butterfat must be mixed with milk that is 2% butterfat to get 18 gallons of milk containing 4% butterfat? I am having trouble setting up th

Question 493651: How many gallons of cream that is 20% butterfat must be mixed with milk that is 2% butterfat to get 18 gallons of milk containing 4% butterfat?
I am having trouble setting up the equation. We were thinking it went something like this...
.02x + .2x = .04(18)
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many gallons of cream that is 20% butterfat must be mixed with milk that is 2% butterfat to get 18 gallons of milk containing 4% butterfat?
----
Equation:
fat + fat = fat
0.02x + 0.20(18-x) = 0.04*18
--------------
Multiply thru by 100
2x + 20*18 - 20x = 4*18
-18x = -16*18
x = 16 gallons
18-x = 2 gallons (amt of cream needed)
========================================
If that method is too confusing try 2 equations with 2 variables:
c is cream
m is milk
----
m + c = 18
0.02m + 0.20c = 0.04*18
-----
Multiply thru 1st by 2
Multiply thru other by 100
---
2m + 2c = 2*18
2m + 20c= 4*18
----
Subtract:
18c = 2*18
c = 2 gallons (amt. of cream needed)
====
Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = gallons of cream needed
Let = gallons of milk needed
given:
(1)
(2)
---------------------
(2)
Multiply both sides of (1) by ,
and subtract (1) from (2)
(2)
(1)

and, since
(1)
1)
2 gallons of cream are needed
16 gallons of milk are needed
check:
(2)
(2)
(2)

OK
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