You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you need to add to the mixture

1.25 cups

Step-by-step explanation:

The inicial concentration of the 10 cups of mixture is 10% of white vinegar and 90% water. We can then calculate the number of cups of white vinegar in the mixture:

Amount of white vinegar = 10% of 10 cups = 1 cup of white vinegar

Concentration of white vinegar = 1/10 (cups of white vinegar over cups of mixture

So, if we want to add white vinegar (x cups) until the mixture will be 20% white vinegar and 80% water, we have that:

Amount of white vinegar = (1+x) cups of white vinegar

Total number of cups in the mixture = 10+x

Concentration of white vinegar = 20% = (1+x) / (10+x)

(1+x) / (10+x) = 0.2

1 + x = 2 + 0.2x

0.8x = 1

x = 1.25 cups

You need to add 1.25 cups of white vinegar.