Blend It All

Algebra Level 3

A young bachelor came for a job interview in a large beverage company. During the interview, the interviewer showed him 2 bottles of liquor on the table.

Interviewer : Here are 2 different liquor solutions: one with 15% alcohol in volume and another with 40%, as labeled. If the client demanded the product degree of 25%, how would you proceed?

The applicant measured the volumes in both bottles, which turned out to be co-prime integer values in pints, with more volume in the higher degree one.

Applicant : All I need is pure water and a small, empty barrel.

All were supplied as he asked, and then the applicant poured the pure water into the lesser degree solution until both bottles now had the same volume. Finally, he poured out all the liquid from both bottles into the barrel and blended it altogether.

Applicant : Now the client's got his liquor served.

Admiring, they both shook hands, and the job was accepted.

How much liquor (in pints) was there in that barrel?

The answer is 6.

1 solution

Worranat Pakornrat
Dec 5, 2018

Let $x$ be the amount of pints in 15% bottle and $y$ be that in 40% one. It is clear from the question that the pure water volume equals $y-x$ , and total volume in the barrel is $2y$ , for it was double the 40% bottle in the question.

Hence, we can set up equation for the amount of alcohol volume, before and after the blend:

$\dfrac{15x}{100} + \dfrac{40y}{100} = \dfrac{25(2y)}{100}$

$3x + 8y = 10y$

$3x = 2y$

Since $x,y$ are co-prime integers, we can conclude $x = 2$ and $y=3$ , and so the water volume used equals $3-2 = 1$ pint.

Thus, there will be $1+2+3 = \boxed{6}$ pints of liquor in the barrel.

Blend It All

The answer is 6.

1 solution

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