In NY the ratio of private homes to apartment is 3:5 . If all the apartments are brick made and 1/10 of the private homes are wooden what is the maximum portion of houses that may be brick made?
a 15/16
b 5/8
To find the maximum portion of houses that may be brick made, we need to determine the ratio of brick houses to the total number of houses (both private homes and apartments).
Let's start by assuming there are 3x private homes and 5x apartments, based on the given ratio of 3:5.
Out of the 3x private homes, 1/10 are wooden, which means (1/10) * 3x = 3x/10 private homes are wooden.
Therefore, the number of brick private homes is: 3x - (3x/10) = (30x/10) - (3x/10) = (27x/10).
The number of brick apartments is given as 5x.
To find the total number of houses, we add the number of brick private homes and the number of brick apartments: (27x/10) + 5x = (27x + 50x)/10 = (77x)/10.
Therefore, the ratio of brick houses to the total number of houses is: ((27x/10) + 5x) / ((77x)/10) = (32x/10) / (77x/10) = 32x/77x = 32/77.
Thus, the maximum portion of houses that may be brick made is 32/77.
Therefore, the correct answer is not among the options provided.