Draining the Antifreeze

A Very Confusing Mixture Problem

The Problem

Your car can hold 12 liters of anti-freeze.

It currently has a 10% antifreeze solution.

Winter is on the way!

How much antifreeze do you need to drain and replace with pure antifreeze to make it a 25% solution?

The Confusion

1. Drain? We have only done problems where we add things together. Drain? What am I supposed to do with drain?

2. Pure antifreeze? Why did they say pure antifreeze?

The Confusion

1. Drain?

1. We are mentally going to drain all the antifreeze and put it in a pail.

2. Then we’re going to add antifreeze from the pail and some pure antifreeze.

3. Voila! - a familiar mixture problem.

2. Pure anti-freeze? The percentage of antifreeze in pure anti-freeze is 100%.

Let’s make our boxes

#

liters%

Liters antifreeze

old mix x 10 10x

Pure 12 - x 100 100( 12 – x)

New mix 12 25 300

Let’s make our equation

10x + 100( 12 – x) = 300

Liters antifreeze

Antifreeze in old mix

10x

Antifreeze in pure 100( 12 – x)

Antifreeze in new mix

300

Now let’s solve

10x + 100( 12 – x) = 300

10x + 1200 - 100x = 300

- 90x = 300 – 1200

- 90x = - 900

x = 10

Now let’s check

We’ve kept 10 liters of our old 10% solution. That’s 1 liter of antifreeze.

We have 2 liters of the pure stuff. That’s 2 liters of antifreeze.

1 + 2 = 3 liters of antifreeze.

We wanted 25% of the 12 liters to be antifreeze.

25% of 12 = .25 ( 12 ) = 3 Hooray!

Don’t Allow Brain Drain!

Drain?Drain it all into a pail and mix it back in like a regular problem.

Pure Antifreeze?100% antifreeze