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 20-ounce econo-size bottle contained 3 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 it use in an econo-size bottle ?
A)Rose oil: 3 Oil of fermented prunes: 7
Alcohol: 10
B) Rose oil: 3
Oil of fermented prunes: 7
Alcohol: 11
C) Rose oil: 10
Oil of fermented prunes: 7
Alcohol: 3
D) Rose oil: 10
Oil of fermented prunes: 3
Alcohol: 7
E) Rose oil: 4
Oil of fermented prunes: 7
Alcohol: 11

Question

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 20-ounce econo-size bottle contained 3 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 it use in an econo-size bottle  ?
A)Rose oil: 3 Oil of fermented prunes: 7
Alcohol: 10
B) Rose oil: 3
Oil of fermented prunes: 7
Alcohol: 11
C) Rose oil: 10
Oil of fermented prunes: 7
Alcohol: 3
D) Rose oil: 10
Oil of fermented prunes: 3
Alcohol: 7
E) Rose oil: 4
Oil of fermented prunes: 7
Alcohol: 11

Quizplus · Accepted Answer

The total volume of the bottle is 20 ounces. Let's denote the amount of rose oil as R, oil of fermented prunes as P, and alcohol as A. We have three pieces of information:1. A = P + 32. A = R + P3. R + P + A = 20Substituting the first equation into the second gives us P + 3 = R + P, which simplifies to R = 3. Substituting R = 3 and A = P + 3 into the third equation gives us 3 + P + (P + 3) = 20, which simplifies to 2P + 6 = 20, and further to 2P = 14, so P = 7. Therefore, A = P + 3 = 7 + 3 = 10. This matches option A: Rose oil: 3, Oil of fermented prunes: 7, Alcohol: 10.

The Fancy French Perfume Company Recently Had Its Secret Formula