SOLUTION: A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are poets are there?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are poets are there?      Log On


   

Question 75007: A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are poets are there?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Look at it this way ... for every 8 people, 5 are novelists. Therefore, you can write the
proportion:
.
5%2F8+=+x%2F24
.
You can read this as, "5 out of every 8 is the same as x out of 24." x will be the number
of novelists enrolled in a group of 24 people.
.
In proportions such as this you can solve for the unknown by first cross multiplying.
This means multiply the numerator of the first fraction by the denominator of the second fraction.
Then multiply the denominator of the first fraction times the numerator of the second fraction.
Then set the two products equal and solve for x.
.
This translates to:
.
5%2A24=+8%2Ax
.
Multiply out the left side to get 120. This makes the problem:
.
120+=+8%2Ax
.
Divide both sides by 8 and you get:
.
120%2F8+=+x which simplifies to just x+=+15
.
So, in a group of 24 persons, 15 will be novelists. That means the remaining 9 persons must
be poets. So, we can now check the ratio of novelists to poets and see if it is 5 to 3 as
stated in the problem.
.
15%2F9+=+5%2A3%2F%283%2A3%29+=+5%2Across%283%29%2F%283%2Across%283%29%29+=+5%2F3. The answer checks.
.
Hope this helps you to understand proportions. And don't forget that you can solve proportions
by cross multiplying.