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# help

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Dr. Graham currently has two acid solutions. She only has a 60% acid solution and a 20% acid solution in her lab. Dr. Graham needs 30 L of a 50% acid solution to conduct an experiment. How many liters of each solution should she mix together

Feb 19, 2020

#2
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Let  x  be the amount  of the  60%  solution  in L

Let  30 - x  be the amount of the 20%  solution in  L

So

.60x  + .20(30 - x)   = .50(30)    simplify

.60x  + 6  - .20x  = 15

.40x  +  6   = 15     subtract 6 from both sides

.40x  = 9     divide both sides by  .40

x  =  22.5  =   amount of  60% solution (in L)

30  - x =  7.5  =  amount of  20% solution ( in L )   Feb 20, 2020
edited by CPhill  Feb 20, 2020

#1
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0.6x*0.2(1-x)=0.5
Factor out

0.6x*0.2-0.2x=0.5

Move x to one side

0.6x-0.2x=0.5-0.2

0.4x=0.3

x=0.3/0.4
x=0.75

So we need 0.75 of 60% solution and 0.25 (i.e 1-0.75) of 20% solution

Feb 19, 2020
#2
+1

Let  x  be the amount  of the  60%  solution  in L

Let  30 - x  be the amount of the 20%  solution in  L

So

.60x  + .20(30 - x)   = .50(30)    simplify

.60x  + 6  - .20x  = 15

.40x  +  6   = 15     subtract 6 from both sides

.40x  = 9     divide both sides by  .40

x  =  22.5  =   amount of  60% solution (in L)

30  - x =  7.5  =  amount of  20% solution ( in L )   CPhill Feb 20, 2020
edited by CPhill  Feb 20, 2020