SOLUTION: In a chemical laboratory one carboy contains 12 gallons of acids and 18 gallons of water. Another carboy contains 9 gallons of acid and 3 gallons of water. How many gallons must be

Question 306669: In a chemical laboratory one carboy contains 12 gallons of acids and 18 gallons of water. Another carboy contains 9 gallons of acid and 3 gallons of water. How many gallons must be drawn from each carboy and combined to form a solution that is 7 gallons acid and 7 gallons water?
Choices:
a.) 10 gals from first carboy and 4 gals from second carboy
b.) 9 gals from first carboy and 5 gals from second carboy
c.) 8 gals from first carboy and 6 gals from second carboy
d.) 11 gals from first carboy and 3 gals from second carboy
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a chemical laboratory
A. one carboy contains 12 gallons of acids and 18 gallons of water.
B. Another carboy contains 9 gallons of acid and 3 gallons of water.
-----------------
How many gallons must be drawn from each carboy and combined to form a solution that is 7 gallons acid and 7 gallons water?
----
Acid Equation: 12A + 9B = 7 gallons
Water Equatio: 18A + 3B = 7 gallons
--------------------------------------
Solve by elimination:
Multiply thru 2nd equation by 3 to get:
54A + 9B = 21
----------------------
Subtract the 1st equation from that and solve for A:
42A = 14
A = 1/3
1/3 1st carboy gives 4 gals acid and 6 gals water
------
Substitute into 18A + 3B = 7 and solve for B:
18(1/3) + 3B = 7
3B = 1
B = 1/3
1/3 2nd carboy give 3 gals acid and 1 gal of water
==============================
1/3 of 1st carboy = 10 gals
1/3 of 2nd carboy = 4 gals
================================
Cheers,
Stan H.
=====================================
Choices:
a.) 10 gals from first carboy and 4 gals from second carboy
b.) 9 gals from first carboy and 5 gals from second carboy
c.) 8 gals from first carboy and 6 gals from second carboy
d.) 11 gals from first carboy and 3 gals from second carboy

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