SOLUTION: A chemist has two acid solutions. Solution A contains 10% acid, and Solution B contains 30% acid. He will mix the two solutions to make 10 liters of a third solution, Solution C, c

Question 964428: A chemist has two acid solutions. Solution A contains 10% acid, and Solution B contains 30% acid. He will mix the two solutions to make 10 liters of a third solution, Solution C, containing 25% acid.
The system of equations shown can be used to represent this situation.
x + y = 10
0.10x + 0.30y = 2.5
What is the number of liters of solution B the chemist mixes with solution A to create solution C containing 25% acid?
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
A=liters of Solution A; B=liters of Solution B
A+B=10
A=10-B Use this to substitute for A
0.10A+0.30B =0.25(10) Substitute for A from above.
0.10(10-B)+0.30B=2.5
1-0.10B+0.30B=2.5 Subtract 1 from each side.
0.20B=1.5 Multiply each side by 5.
B=7.5 ANSWER 1:The chemist should use 7.5 liters of solution B.
A=10-B=10-7.5=2.5 ANSWER 2: The chemist should use 2.5 liters of Solution A.
CHECK:
0.10(A)+0.30(B)=0.25(10)
0.10(2.5)+0.30(7.5)=2.5
0.25+2.25=2.5
2.5=2.5

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The second, concentration equation:

should become
------this will be easier to work with.

You now have the system

Simplifiable to

Simply subtract the first equation from the second equation to eliminate x.

; and from the necessary 10 liters of the 10%, you have .
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