SOLUTION: The Fancy French Perfume Company recently had its secret formula divulged. It turned out that it was using, as the three ingredients, rose oil, oil of fermented prunes, and alcohol

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Question 1110992: The Fancy French Perfume Company recently had its secret formula divulged. It turned out that it was using, as the three ingredients, rose oil, oil of fermented prunes, and alcohol. Moreover, each 26-ounce econo-size bottle contained 8 more ounces of alcohol than oil of fermented prunes, while the amount of alcohol was equal to the combined volume of the other two ingredients. How much of each ingredient did the company use in an econo-size bottle?
Answer by ikleyn(52873) About Me  (Show Source):
You can put this solution on YOUR website!
.
R = rose oil,  P = oil of Prunes,  A = alcohol, each ingredient in ounces.


It is easy to setup this system of 3 equation in 3 unknowns

R + P + A = 26,    (1)
    P - A = -8,    (2)
A = R + P.         (3)


But there is more easy way to solve.


Since  A = R + P according to (3), it means that   and


A = 13         (half of the volume),


Then from (2)  P = -8 + A = -8 + 13 = 5.


Finally,  from (3)  R = A - P = 13 - 5 = 8.


So, the secret is discovered:  A = 13,  R = 8,  P = 5  ounces.

Solved.