Mixture of Spices

Welcome! You are encouraged to register with the site and login (for free). When you register, you support the site and your question history is saved.

Mixture A of spices is 60 percent parsley and 40 percent oregano by weight. Mixture B of spices is 25 percent parsley and 75 percent thyme. If a mixture of A and B contains 35 percent parsley, approximately what percent of the weight of the mixture is A?

Review: Mixture of Spices


Explanation

We can write a weighted average for the amount of parsley in the final mixture. In general, where a weighted average is possible, it will be the fastest route to solving a question. We can call X the proportion of mixture A.



Thinking of this as an average, we can get a sense of how X and 1 - X compare. 0.60 is 0.25 away from the final value, whereas 0.25 is only 0.10 away from the final value. For the second term to have the influence, it has, 1 - X must be somewhere around 2.5 times the value of X. So X is a pretty modest percentage. Even (B) looks too big; the odds are strong that (A) is the answer. We can confirm:





This statement is not quite correct, but it's quite close; indeed, the question says "approximately."

The correct answer is (A).


If you believe you have found an error in this question or explanation, please contact us and include the question title or URL in your message.
Continue »