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### Ratios and Mixtures

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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

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?

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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

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

Good luck.

- Doctor Jaffee, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Ratio and Proportion
Middle School Word Problems

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