Respuesta :
Answer:
C. 6
Step-by-step explanation:
Let x liters represent 70% of the solution.
Let us assume that solution is diluted with water, which has a 0% strength.
We have been given that you have been asked by the Pharmacist to prepare 3 liters of a 30% strength solution. Your pharmacy stocks the active ingredient in 8 oz bottles of 70% strength.
The amount of water would be 3 liters minus liters of 70% solution that is [tex]3-x[/tex].
Now we can set an equation where 70% of x plus 0% of [tex](3-x)[/tex] is equal to 30% of 3 liters.
[tex]70\%\cdot x+0\%(x-3)=30\%\cdot 3[/tex]
[tex]\frac{70}{100}\cdot x+\frac{0}{100}(x-3)=\frac{30}{100}\cdot 3[/tex]
[tex]0.70\cdot x+0=0.30\cdot 3[/tex]
[tex]0.70x=0.90[/tex]
[tex]\frac{0.70x}{0.70}=\frac{0.90}{0.70}[/tex]
[tex]x=1.2857[/tex]
Since our amount is in liters, so we need to convert 1.2857 liters into oz.
1 liter = 33.814 oz
1.2857 liters = 1.2857*33.814 oz = 43.4746598 oz
Since each bottle contains 0 oz, so we will divide 43.4746598 by 8 to find the number of bottles.
[tex]\text{Required number of bottles}=\frac{43.4746598}{8}[/tex]
[tex]\text{Required number of bottles}=5.43433[/tex]
Since we cannot open 0.43433 of a bottle, so we need to open 6 bottles and option C is the correct choice.
