Asked by Math H of the medcater

A pharmacist wants to mix two solutions to obtain 100 cc of a solution that has an 8% concentration of a certain medicine. If one solution has a 10% concentration of the medicine and the second has a 5% concentration, how much od each of these solutions should she mix?
I am terrible with word problems and I just can't understand what's going on!? I don't know if this would help but we are currently on Linear Models, Equations and Inequalities, using substitution, elimination and graphical methods.
Answered by Reiny
So I will use two variables in the solution

let the amount of 10% solution used be x cc
let the amount of 5% solution be y cc

"A pharmacist wants to mix two solutions to obtain 100 cc" ---> x + y = 100

the new solution must contain 8% , so .08(100)

2nd equation:
.10x + .05y = .08(100)
I would multiply this by 100 to get rid of those nasty decimals
10x + 5y = 800
now divide by 5
2x + y = 160

so now we have

2x + y = 160
x + y = 100
subtract them:
x = 60
back in the first:
60+y = 100
y = 40

So they need 60 cc of the 10% solution and
40 cc of the 5% solution

check:
60+40 = 100, check!
.10(6) + .05(4) = .08(100
6+2 = 8 , check!
Answered by Math Hater
Thank you so much! My problem was that when I multiplied .08 by 100 I got 8 instead of the 800...so I wouldn't get the right answer...but I just went with it!(:
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