Georgina wants to make a 42% citric acid solution. if she has 0.5 liters of water, how many liters of a 49% citric acid solution should she add?

Georgina should add 3 liters of 49% citric acid solution.

Step-by-step explanation:

let x be the liters of 49% solution that Georgina should add. Then after she has added 0.5 liters of water, the total liters of solution she has will be

and 42% of this should be the solute:

and since adding water does not add any solvent, this amount must come from the 49% citric acid solution; therefore

Solving for we get:

This the amount of 49% citric acid solution Georgina must add.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11