Question

How much water must be added to 12 L of a 40% solution of alcohol to obtain a 30% solution?

A. .5 L
B. 5 L
C. .4 L
D. 4 L

Answer 1

@jim_thompson5910

Answer 2

you have 12 L of a 40% alcohol solution

how much pure alcohol do you have?

Answer 3

C?

Answer 4

40% of 12 = ??

Answer 5

wait sorry i waking thinking about making the % in to a decimal

Answer 6

40% of 12 = 0.4*12 = ??

Answer 7

its 4.8

Answer 8

ok so you have 4.8 L of pure alcohol

Answer 9

let x = amount of water you want to add to the solution

Answer 10

your initial solution is 12 L

when you add x liters of water, you jump to 12+x liters total (of mixed solution)

Answer 11

the pure alcohol amount stays the same...so you still have 4.8 L of pure alcohol because you aren't adding/subtracting any alcohol

Answer 12

so were trying to take away pure alcholo right ? to be 30 %

Answer 13

no

Answer 14

you don't add or remove any amount of alcohol

Answer 15

you just add more water to dilute the solution

to make the alcohol percentage lower

Answer 16

and how do we do that ?

Answer 17

what this means is that

[ (amount of pure alcohol)/(total amount) ]*100 = percentage of alcohol in solution

[ (4.8)/(12+x) ] * 100 = 30

(4.8)/(12+x) = 30/100

(4.8)/(12+x) = 0.3

4.8 = 0.3(12+x)

4.8 = 3.6+0.3x

4.8-3.6 = 0.3x

1.2 = 0.3x

0.3x = 1.2

x = 1.2/0.3

x = 4

So you need to add 4 liters of water to turn 12 L of a 40% solution into a 30% solution