Question

For every person who actually has the flu, there are 6 persons who have flu-like symptoms resulting from a cold. If a doctor sees 40 patients, write and solve a proportion to determine how many of these you would expect to have a cold?

Answer 1

`34 2/7" "` This is an unexpected proportion. Is the question correct?
I suppose you could round this up to 35 people

Explanation:

Breaking the question down into component parts:

For every person `-> 1`
There are `-> 1+?`
6 persons `-> 1+6`

Note that the question wording is very specific about the proportions.

It is declared that the number of people with flue like symptoms due to a cold is 6.

It is also declared that the corresponding number of people with genuine flue is 1

................................................................................

Combined count of people with genuine flue symptoms and those with flue like symptoms is 1 + 6 = 7

This gives the fractional proportion of `1/7` that probability suggests have flue.

Note that probability (statistics) is not certainty. It is a strong indicator.

So the expected proportion of genuine flue cases from 40 patients is: `1/7xx40`

Thus those that probably have a cold is

`(1-1/7)xx40" " ->" " 6/7xx40" "=" "34 2/7` people

`color(green)("You can not have "2/7" of a person so perhaps the counts of the ")` `color(green)("people in the question are wrong.")`