SOLUTION: How so you solve this problem? Photoworks.com charges $7.00 forr processing a 24-exsposure roll and $10.00 for processing a 36-expsosure. After Karens photography field trip, she

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Question 27818: How so you solve this problem? Photoworks.com charges $7.00 forr processing a 24-exsposure roll and $10.00 for processing a 36-expsosure. After Karens photography field trip, she sent 19 rolls of film to photoworks and pid $151 dollars for processing. How many rolls of each type were processed
Answer by bmauger(101) (Show Source):
You can put this solution on YOUR website!
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:

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:

Now we have to solve these equations. The easiest way is using substitution, so we'll rewrite the first equation for x:
subtract y from both sides:

Now we can substitute 19-y for x in the second equation:
Substitute:
Distibute:
Rearrange:
Divide:

So she'll process 6 36-exposure rolls, and 19-6= 13 rolls of 24 exposures.
Check.