Question 1209265
<br>
x = # of $14 pads
y = # of $5 pads
z = # of 50-cent pads<br>
The total number of pads was 54:
{{{x+y+z=54}}}<br>
The total cost was $54:
{{{14x+5y+.5z=54}}}<br>
With the equations in this form, I find it easiest to solve using elimination.<br>
Multiply the second equation by 2 and compare to the first using subtraction:<br>
{{{28x+10y+z=108}}}
{{{x+y+z=54}}}
{{{27x+9y=54}}}
{{{3x+y=6}}}<br>
There are formal methods for finding the complete set of solutions to this equation. However, since the numbers are small and all unknowns have positive integer values, the solution is simple -- the only solution in positive integers is x=1 and y=3, which leads to z=50.<br>
# of $14 pads: 1
# of $5 pads: 3
# of 50-cent pads: 50<br>
ANSWER: 50-3 = 47<br>