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How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze?

To obtain a 35% antifreeze solution, □ gallon(s) of water should be added
(Simplify your answer.)

Respuesta :

Assume that x gallon water is added: 35% antifreeze
= 1 / (x + 1) = 0.35 
1 = 0.35 x + 0.35 
0.65 = 0.35(x) 
x = 1.857 gallons
The answer is 1.89 gallons of waters should be added to 1 pure antifreeze to obtain a solution that is 35% antifreeze.
JeanaShupp

Answer: 1.9 gallon

Step-by-step explanation:

Let 'x' be the amount of water that needed to be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze.

Total mass of solution = 1+x

Ratio of amount of antifreeze to the total solution : [tex]\dfrac{1}{1+x}[/tex]

Ratio of value of antifreeze to the total solution : [tex]\dfrac{0.35}{1}[/tex]

The proportion of the amount of antifreeze to the total solution will be :

[tex]\dfrac{1}{1+x}=\dfrac{0.35}{1}\\\\\Rightarrow\ 1+x=\dfrac{1}{0.35}=1.85714285714\approx2.9\\\\\Rightarrow\ x=2.9-1=1.9[/tex]

Hence, the amount of water that is needed to be added =1.9 gallon