Alcohol solution word problem

Question

you need a 55% alcohol solution. On hand, you have a 630 mL of a 30% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?

Answer 1

The answer is 350.

 

This is a balance equation: what you put in has to equal what you get out.

 

630(.30) + (UNKNOWN AMOUNT)1.00 = (630 + UNKNOWN AMOUNT).55

 

Note: "Pure" = 100% = 1.00; UNKNOWN AMOUNT = x

 

630(.3) + x(1) = (630 + x).55

 

Simply both sides, including distributive property on the right side of the equation.

 

189 + x = 346.5 + .55x

 

Subtract 189 AND .55x from both sides, combining like terms.

 

.45x = 157.5

 

Divide both sides by .45 to solve for x.

 

x = 350 = UNKNOWN VALUE

 

 And the result would be a 980ml solution: 630 + 350.