Question

X percent of 1 unit alcohol is mixed with 3 units of Y percent alcohol to give 60% alcohol. If X > Y, how many integers:

a. 1
b. 2
c. 3
d. 4

Answer 1

The question asks to calculate the relationship between two percentages (X and Y) when they are mixed to form a 60% alcohol mixture, considering that X is greater than Y and the mixture is in a specific ratio determined by the units of alcohol mixed.

Step-by-step explanation:

The given problem discusses mixing different concentrations of alcohol to achieve a mixture with a specified final percentage. It involves concepts from algebra and percentage concentration calculations which are common in chemistry but here are used purely for mathematical purposes.

Let's assume X is the percentage of alcohol in the first unit and Y is the percentage of alcohol in the other three units. According to the problem, when these are mixed, the resulting mixture is 60% alcohol. The equation to represent this situation can be expressed as follows:

(X% × 1 unit) + (Y% × 3 units) = 60% × (1 unit + 3 units)

Now, simplifying this equation will help us find the relationship between X and Y.