word problem set up

Question

angel has 5% alcohol soulution and 20% alcohol solution. She needs 30 liters of a 10% alcohol solution. How many liters of each should she mix to get 30 liters?

Answer 1

Method 1.

x = amount of 5% solution

30-x = amount of 20% solution

.05x + .2(30-x) = .1*30

Solve for x,

x = 20 liters

30-x = 10 liters

 

Method 2.

Quick way: Using difference proportion.

The amount of 5% alcohol soltion = [10/(5+10)]*30 = 20 liters

The amount of 20% alcohol soltion = [5/(5+10)]*30 = 10 liters

 

Answer 2

Hi Bre!

10% of 30L means 3L of pure alcohol ...

A sure way to get 30L of 10% is to mix 15L of 20% with 15L water: cuts in 1/2

I would next try 10L of 20% and 20L of 5% ==> 2L + 1L, or 3L of pure stuff :)