SOLUTION: A pharmacist is making an antiseptic of iodine and alcohol. The iodine/alcohol mixture he now has is 5% iodine. He wants a mixture that is 6% iodine How much of 10% iodine solution

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Question 266462: A pharmacist is making an antiseptic of iodine and alcohol. The iodine/alcohol mixture he now has is 5% iodine. He wants a mixture that is 6% iodine How much of 10% iodine solution and how much of the original antiseptic should he mix to make 50ml of the new antiseptic.
ps. it is solving for two variables and i need it it a box to set up the information.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of 10% iodine solution needed
Then 50-x=amount of the original antiseptic (5% iodine) needed
Now we know that the amount of pure iodine in the 10% solution (0.10x) plus the amount of pure iodine in the original antiseptic that is used (0.05(50-x)) has to equal the amount of pure iodine in the final mixture (0.06*50). So, our equation to solve is:
0.10x+0.05(50-x)=0.06*50 get rid of parens
0.10x+2.5-0.05x=3 subtract 2.5 from each side
0.10x+2.5-2.5-0.05x=3-2.5 collect like terms
0.05x=0.5 divide each side by 0.05
x=10 ml-----------------amount of 10% iodine needed
50-x=50-10=40 ml -----amount of original antiseptic needed
CK 0.10*10+40*0.05=0.06*50
1+2=3
3=3
Hope this helps----ptaylor