Ratios and Mixtures

Date: 05/10/2001 at 00:16:55
From: Hollie
Subject: Ratios

Sue needs to mix up a potion for her client. The recipe calls for 
140ml of turpentine, 160ml of India ink, and 50ml of honey.  

Sue pours 140ml of turpentine into an empty 350ml bottle. As she is 
adding the India ink her cat distracts her, and she pours too much. 
She only realizes her mistake when she finds that the bottle is 
already full before she can add the honey. 

Sue does a quick calculation, thoroughly mixes the potion, and pours 
some of the turpentine and ink mixture down the sink. She replaces 
what she has poured out with a honey-and-turpentine mixture that 
results in the final mixture in the bottle matching what is called for 
in the recipe.

a. In what ratio must Sue have mixed the honey and turpentine 
   together for the replacement?

b. If Sue poured 70ml of the turpentine-and ink-mixture down the sink, 
   how much of each ingrediant was wasted?

Please show me and explain the answer. Thanks heaps.

Date: 05/10/2001 at 14:48:36
From: Doctor Jaffee
Subject: Re: Ratios

Hi Hollie,

Here is how I approached your problem.  If Sue poured 140 ml of 
turpentine into the 350 ml container, then she must have poured 210 ml 
of ink, since 350 - 140 = 210.

When she mixed up the turpentine and ink, 140/350 = 2/5 of the mixture 
was turpentine, and the other 3/5 was ink.

So, if she poured out x ml of the mixture, she poured out (3/5)x ml 
ink and (2/5)x ml turpentine.

What was remaining then was 350 - x of the mixture, of which 
(2/5)(350 - x) ml was turpentine and (3/5)(350 - x) ml was ink.

When Sue replaced what she had discarded, she mixed together honey and 
turpentine. If she didn't add any more ink, it must mean that the ink 
she already had in the container was 160 ml.

Therefore, (3/5)(350 - x) = 160. You can solve this for x and use the 
result to answer the two questions you asked. Keep in mind that in the 
honey and turpentine mixture that she is about to add, exactly 50 ml 
must be honey.

Give it a try and if you want to check your answers, write back. If 
you are having difficulties, let me know what you have done so far and 
I'll help you out.

Good luck.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/