How much 90% vinegar do you have to add to a gallon of 5% vinegar to get 20% vinegar?

Question

Hint: You want the final percentage of pure vinegar to be 20%. You have 1+x gallons of fluid where x is the number of gallons you add. Think about how much pure vinegar is in those 1+x gallon. 

Answer 1

Hi Giovalise,

 

Let's begin by assigning a letter to represent our unknown:

    x = gallons of 90% solution

 

Now let's write expressions for the amount of vinegar in each solution:

    90% solution = (0.90)(x) gallons of vinegar

    5% solution = (0.05)(1) = 0.05 gallons of vinegar

    20% solution = (0.20)(x + 1) gallons of vinegar

 

Now we can write an equation to show the combining of these vinegar amounts to make up our final vinegar amount and then solve it for our unknown (x):

    (0.90)(x) + (0.05)(1) = (0.20)(x + 1)

    0.90x + 0.05 = 0.20x + 0.20

    0.90x - 0.20x = 0.20 - 0.05

               0.70x = 0.15

                     x = 0.15 / 0.70

                     x = 3/14 gallons of 90% solution

 

With word problems - the old adage is true - divide and conquer !!

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.