excess shortage problem

Question

Rose had some money to buy some plastic files. If she bought 12 files, she would need $8 more. If she bought 9 files, she would be left with $5. How much money did Rose have?

Answer 1

x=amount of money each file cost

9x+5=12x-8

12x-9x=8+5

3x=13

x=13/3

x=$4.333... or $4.333 1/3 for each file (4 and 1/3 dollars for each file)

9*$4.33 1/3+$5=$39+5=$44.00

Rose has $44.00

if she bought 12 files, 12*$4.33 1/3=$52.00, which is $8.00 short

 

Answer 2

If we call the price of the files "x" and the amount of money that Rose has "y," then this problem can be solved by solving the following system of equations:

 

12x = y + 8

9x = y - 5

 

This system can be derived by careful interpretation of the problem. 12 files (12x) cost 8 dollars more than Rose has (y + 8). 9 files (9x) cost 5 dollars less than Rose has (y - 5). From here, the problem can be solved in a number of ways. Since we want to solve for how much money Rose has, we should solve for "y." One way to do this is to use the elimination method, though substitution would also work.

 

Elimination:

 

3(12x = y + 8) => 36x = 3y + 24

4(9x = y - 5) => 36x = 4y - 20

 

Subtract the second from the first to obtain:

 

0 = - y + 44

=> y = 44

 

So Rose has $44. Oddly, this means that the files cost four and one third dollars...

 

Hope this helps!