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?

Question

Nathan Axel · Accepted Answer

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

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.")#

Abigail Allen · Answer

undefined Proportion:

x/40 = 6/1

Solve for x:

x = (40 * 6)/1 = 240

Therefore, you would expect 240 of the 40 patients to have a cold.