SOLUTION: A 40% antifreeze solution and a 70% antifreeze solution is mixed to make 12 gallons of 50% antifrezze solution. How many gallons of each antifreeze solution should be used.

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Question 158343: A 40% antifreeze solution and a 70% antifreeze solution is mixed to make 12 gallons of 50% antifrezze solution. How many gallons of each antifreeze solution should be used.
Found 2 solutions by jojo14344, atique.ah:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
40% a/f = x
70% a/f = y
Number of gallons of x + y equals 12gal
x%2By=12 ------------------> eqn 1
We get, y=12-x ----------> eqn 2
Also,
0.40x%2B0.70y=0.50%2812%29 ----> eqn 3
Substitute eqn 2 in eqn 3:
0.40x%2B0.70%2812-x%29=6
0.40x%2B8.4-0.70x=6
8.4-6=0.70x-0.40x
2.4=0.30x ----> cross%282.4%298%2Fcross%280.30%29=cross%280.30%29x%2Fcross%280.30%29
x=8gal ----------------------> for the 40% a/f
In eqn 2:
y=12-8=4gal ----------------> for the 70% a/f
In doubt? go back eqn 3:
0.40%288%29%2B0.70%284%29=0.50%2812%29
3.2%2B2.8=6
6=6
Thank you,
Jojo

Answer by atique.ah(27) About Me  (Show Source):
You can put this solution on YOUR website!
A 40% antifreeze solution and a 70% antifreeze solution is mixed to make 12 gallons of 50% antifrezze solution. How many gallons of each antifreeze solution should be used.
SOLUTION:
...............GALLONS....................%..........TOTAL
70% AF......... X........................0.7.........0.7X
40% AF..........Y........................0.4.........0.4Y
MIX 50%.....X+Y=12............0.5............0.5*12=6

0.7X+0.4Y=6 EQ 1
X+Y=12 EQ 2
Solve for y and x and get the answer