Question related to Fractions - is this a typo ?

The question is:

Quote:

In a section of a city the ratio of private homes to apartment house dwellings is 5:3 . If all the apartment house dwellings are brick structures and 1/10 of private homes are wooden structures , what is the maximum portion of houses that may be brick..

According to the book the answer is 15/6 but the answer i got is 15/2

Here is how i attempted it

private homes/apartments = 5/3

since 1/10 of private homes is wooden so 9/10 must be brick.

so total brick structures are

3+(9/10)(5)= 15/2

Am i correct and thats a typo in the book or am i missing something

Re: Question related to Fractions - is this a typo ?

maybe I don't understand the question ...

let's say there are 80 total dwellings

according to the ratio 5:3 , there are 50 private homes and 30 apartments

of the 50 private homes, 5 are wood structures and 45 are brick

now the question asks Quote:

what is the maximum portion of houses that may be brick.

do houses include apartments or is the question referring to private homes only?

also, portion of what? the total number of dwellings?

given the above numbers, 75/80 = 15/16 of the dwellings are brick, which is where the "typo" is ... imho.

Re: Question related to Fractions - is this a typo ?

Hello, MikeNoob!

Quote:

In a section of a city, the ratio of private homes to apartment houses is 5:3.

If all the apartment houses are brick structures, and 1/10 of private homes are wooden structures,

what is the maximum portion of houses that may be brick?

According to the book the answer is 15/6 but the answer i got is 15/2.

I believe their answer should be 15/16.

First, no book would (or should) give an *unreduced* fraction for an answer.

Second, it claims that "15 out of 6 houses are brick dwellings" . . . *What?*

. . [Old joke: 5 out of 4 people have difficulty with ratios.]

Here is a "safer" approach . . .

It says that $\displaystyle \tfrac{1}{10}$ of private homes are wooden.

Then up to $\displaystyle \tfrac{9}{10}$ of private homes could be brick.

Let the number of private homes be $\displaystyle 5k.$

Let the number of apartment houses be $\displaystyle 3k.$

. . The total number of dwellings is $\displaystyle 8k.$

$\displaystyle 3k$ apartment houses are brick.

$\displaystyle \tfrac{9}{10}(5k) \,=\,\tfrac{9}{2}k$ private homes are brick (maximum).

Hence, the maximum number of brick dwelings is: $\displaystyle 3k + \tfrac{9}{2}k \:=\:\tfrac{15}{2}k$

Therefore, the ratio of brick dwellings to the total number of dwellings is: .$\displaystyle \frac{\frac{15}{2}k}{8k} \:=\:\frac{15}{16}$

Re: Question related to Fractions - is this a typo ?

@Soroban thanks for the reply but the question isnt asking for a Ratio of brick to the total no of dwellings. This does sounds like a stupid question and i just noticed after u pointed it out that their answer is in an unsimplified form which is "strange". So i think i am going to assume this is a typo for now unless someone actually shows me how they got 15/6. A part of me also agree with you that the author initially intended to ask about the ratio but then messed up at the end,

Re: Question related to Fractions - is this a typo ?

Quote:

In a section of a city the ratio of private homes to __apartment house__ dwellings is 5:3 . If all the apartment house dwellings are brick structures and 1/10 of private homes are wooden structures , **what is the maximum portion **__of houses__ that may be brick.

I think the problem statement's use of the word "houses" includes both private homes (which are houses) and __apartment "houses"__.

... the typo is the missing tens digit in the denominator, 15/6 instead of the correct 15/16.

Re: Question related to Fractions - is this a typo ?