Find the cost of the folder

Question

sam bought three folders and one notebook from the office store and spent $8.25. He went back the next day and bought two more folders and three more folders and three more notebooks and spent $16. if the prices did not change between the days, find the cost of one folder.

Answer 1

Step 1:  For day one the purchases can be written as an equation:  3F + N = 8.25 where "F" is folders and "N" is notebooks.

 

Step 2:  Day two's equation can be written as 5F + 3N = 16 hint: since he bought two more folders and then three more folders, adding them together gives us 5F

 

Step 3:  Day one's equation we can solve for "N" by subtracting 3F from both sides, which leaves us with N=8.25-3F

 

Step 4:  Substitute N=8.25-3F into Day Two's equation for "N" giving us 5F+3(8.25-3F)=16

 

Step 5:  Distribute the 3 across the parenthesis giving us 5F+24.75-9F=16

 

Step 6:  Combine like terms on the left of the equation 5F-9F=-4F.  The equation is now 24.75-4F=16

 

Step 7:  Solve for "F" by subtracting 24.75 from both sides:  -4F=16-24.75, -4F=-8.75

 

Step 8:  Solve for "F" by dividing both sides by -4, F=2.1875. 

 

Since the question is asking how much a folder cost, round the the answer to 2.19.  A folder costs $2.19