Answer:
Let's assume there are a total of x cars in the garage.
From the problem, we know that 1/6 of the cars are black and 3/4 of the cars are silver. That means:
Number of black cars = (1/6) * x
Number of silver cars = (3/4) * x
We also know that the rest of the cars are blue. Therefore:
Number of blue cars = x - [(1/6) * x + (3/4) * x]
Number of blue cars = x - (5/12) * x
Number of blue cars = (7/12) * x
To find the ratio of black to silver to blue cars, we need to express each quantity as a fraction of the total number of cars x:
Number of black cars / x = (1/6) * x / x = 1/6
Number of silver cars / x = (3/4) * x / x = 3/4
Number of blue cars / x = (7/12) * x / x = 7/12
Therefore, the ratio of black to silver to blue cars is:
1/6 : 3/4 : 7/12
To simplify this ratio, we can first convert all the fractions to have the same denominator:
1/6 : 9/12 : 7/12
Then, we can simplify the fractions:
1/6 : 3/4 : 7/12
2/12 : 9/12 : 7/12
1/6 : 3/4 : 7/12
Therefore, the ratio of black to silver to blue cars, in its simplest form, is 1/6 : 3/4 : 7/12.