Question

Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol?

Answer 1

Answer:

13/9l  or 1  4/9 l

Step-by-step explanation:

quantity of alcohol = l liters

we need to made solution of having 45% alcohol by adding water.

45% alcohol means whatever id the total quantity of solution there is 45% alcohol.

Let the total quantity of solution be x.(

then

quantity of alcohol in terms of x = 45% of x = 45/100 x

but we know that quantity of alcohol = l liters

45/100 x = l

x = 100/45 l

Thus, total quantity of solution is 100/45 l,

but in it there is l liters of alcohol.

to find quantity of water we need to subtract quantity of alcohol from total quantity of solution

quantity of water in the solution = 100l/45  - l = (100l - 45l)/45 = 65l/45

quantity of water in the solution = 13/9l = 1 4/9 l -------->answer.

Thus, 1 4/9 liters of water needs to be added to l liters of alcohol to make  a solution of 45% alcohol.