In an area of the city 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?
How to solve this ratio problem?
In an area of the city 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?
How to solve this ratio problem?
Your ratio gives 3 private homes for every 8 (=3+5) houses.
This means as a fraction you have $\displaystyle \frac{3}{8}$ of the total amount of houses are privates homes.
If $\displaystyle \frac{1}{10}$ of the private homes are wooden, then at most, $\displaystyle \frac{9}{10}$ of them are brick. Multiply $\displaystyle \frac{3}{8}$ by $\displaystyle \frac{9}{10}$ to get the fraction of private homes that are brick (or the most that can be brick).
Add to this the fraction of apartments (since they are ALL brick) to get...
$\displaystyle \frac{3}{8} \cdot \frac{9}{10} + \frac{5}{8} = \frac{27}{80} + \frac{50}{80} = \frac{77}{80}$. This is the fraction of houses that are brick (at most).
To convert this to a ratio you get $\displaystyle 7780-77) = 77:3$ which is the maximum ratio of brick houses to wooden houses.
I don't know how it got 15/16. I actually can't figure out why that is.
At most, 90% of the private homes are brick. So that's 9/10 x 3/8 = 27/80.
100% of the apartments are brick. So that's 5/8 = 50/80.
Add those two together and you get 77/80 not 15/16 (=75/80 as the answer suggests)...
Look at it this way.
Say there were 80 houses in total.
The ration tells us that 30 would be private homes and 50 would be apartments.
10% of the private homes are wooden which makes 3.
All 50 apartments are brick and the remaining 27 private houses are unknown which could mean that all 27 are brick.
Hence a maximum of 77 brick houses out of 80.
Hmmm....I'm not a maths expert but let's see what we get if we reverse the ratios. Perhaps there was a communication error.
$\displaystyle p:a=3:5$
$\displaystyle \frac {1}{10} $of a=wooden
$\displaystyle \frac{1}{10}\times\frac{5}{8}=\frac{5}{80}$
= number of wooden.
number of brick = 1-number of wooden
$\displaystyle =\frac{75}{80} = \frac{15}{16} $
Edit: Are you sure you wrote the ratio the correct way around? The way you wrote it suggests that the person above has the correct answer.