Algebra worded problem

Question

Due to the renovation of the male medical ward patients were housed in a nearby facility. A large room housed 48 patients. The number of patients in each row is 10 less than twice the number of rows. Find the number of rows& number of patients per row.

Answer 1

There are two equations that can be formed from the given information

 

Let R = the number of rows and P = the number of patients in a row

 

R·P = 48

P = 2R - 10

 

Substitute the second expression (2R - 10) in for P in the first equation

 

R·(2R -10) = 48

2R² - 10R = 48

2R² - 10R - 48 = 0

 

Divide everything by 2

 

R² - 5R - 24 = 0

Factor this

(R - 8)(R + 3) = 0

 

When you set each factor equal to zero you get R = 8 or R = -3

but we can't have a negative number of rows so R = 8

 

This means there are 8 rows of patients and therefore 6 patients in each row.    :)