Simple Real-Life Math Question

[hermitsoul]

Hi, usually I can figure these things out but this one is making me a little crazy and I don't want to get it wrong, as the correct result means excellent cleaning power and the incorrect result means a nasty corrosive.

Household vinegar is 5% vinegar (assuming that is 95% water). If I have 80% vinegar (assuming it is 20% water), what fraction of an ounce of 80% vinegar must I add to a gallon (128 ounces) of water to make 5% vinegar solution? Or what would the appropriate ratio of parts vinegar to parts water be?

Thanks!

 

[Deleted member 4993]

Hi, usually I can figure these things out but this one is making me a little crazy and I don't want to get it wrong, as the correct result means excellent cleaning power and the incorrect result means a nasty corrosive.

Household vinegar is 5% vinegar (assuming that is 95% water). If I have 80% vinegar (assuming it is 20% water), what fraction of an ounce of 80% vinegar must I add to a gallon (128 ounces) of water to make 5% vinegar solution? Or what would the appropriate ratio of parts vinegar to parts water be?

Thanks!

Suppose you add x gallons of 80% vinegar to 1 gallon of water

now you have vinegar concentration = (0.8*x)/(x+1) ← you want this to equal to 0.05 (or 5%)

so

0.05 = (0.8*x)/(x+1)

solve for 'x' from above (obviously x < 1)

However, measuring out 'x' - accurately - can be a different issue

 

[Ishuda]

Same thing but more general
0.8 V = 0.05 (V + W)
where V is the 80% vinegar solution and W is the amount of water. Solve to get
W = 15 V
So mix in a 1 V to 15 W ratio. For example 120 oz of water and 8 oz of 80% vinegar solution to make a gallon of 5% vinegar solution.

 

[hermitsoul]

Thank you both so much--I really appreciate it!