# healthcare statistics problem

#### Lspencer2121

##### New member
I need help setting this problem up.

6 out of 10 patients discharged in 3 days or less, 12,000 admissions, determine how many were hospitalized over 3 days.

Thanks for the help.

#### MarkFL

Staff member
If 6 out of 10 patients are discharged in 3 days or less, then how many out of ten are hospitalized for more than 3 days?

#### Lspencer2121

##### New member
I appreciate the help but I am still clueless. I know 6/10 is a ratio, which would convert to 3/5, converts to 0.6. My thought is 0.6/12000 Am I correct?

Thanks again for the help.

#### MarkFL

Staff member
If 6 out of 10 patients are discharged in 3 days or less, then 4 out of ten are hospitalized for more than 3 days.

This comes from the fact that 10 out of 10 are either discharged in 3 days or less or are hospitalized for more than 3 days. These two conditions cover everyone. So, if we let $x$ be the number out of ten that are hospitalized for more than 3 days, we must have:

$$\displaystyle 6+x=10$$

$$\displaystyle x=4$$

In a total of 12,000 admissions, there are 1200 groups of 10. In each of these 1200 groups, 4 of the 10 will have been hospitalized for more than 3 days. So, we have 1200 groups of 4...how many is this?

Thank you! 4800.

#### MarkFL

Yes, that's correct! $$\displaystyle 40\%\cdot12000=\frac{40}{100}\cdot12000=40\cdot120=4800$$