Question 27818
This is a type of problem solved by 2 simultaneous linear equations.  You can tell this because you are trying to solve for two unknowns (# of 36-rolls & # of 24-rolls) Let x = the number of 24-exposure rolls that Karen submits, and y equal the number of 36-rolls submitted.  From the problem, we are told that the total number of rolls is 19. So the number of 24-rolls (x) and the number of 36-rolls (y) must add up to 19. Or:
{{{x+y=19}}}
But we can't yet solve this for x or y without knowing something more about them. The other part of the problem says she paid $151 for the total. The amount she'll pay for 24 exposure rolls (x) will be $7/roll or 7x. The amount she'll pay for 36-rolls is $10/roll or 10y.  The total she'll pay is the sum of these two amounts, or:
{{{7x+10y=151}}}
Now we have to solve these equations.  The easiest way is using substitution, so we'll rewrite the first equation for x:
{{{x+y=19}}}subtract y from both sides:
{{{x=19-y}}}
Now we can substitute 19-y for x in the second equation:
{{{7x+10y=151}}}Substitute:
{{{7(19-y)+10y=151}}}Distibute:
{{{133-7y+10y=151}}}Rearrange:
{{{3y=18}}}Divide:
{{{y=6}}}
So she'll process 6 36-exposure rolls, and 19-6= 13 rolls of 24 exposures.
{{{13*7+6*10=151}}}Check.