SOLUTION: PhotoLab charges $9.00 for processing a 24-exposure roll of film and $12.00 for processing a 36-exposure roll. After their class trip, Mr. Renkens' 8th grade class sent 22 rolls o

Question 948328: PhotoLab charges $9.00 for processing a 24-exposure roll of film and $12.00 for processing a 36-exposure roll. After their class trip, Mr. Renkens' 8th grade class sent 22 rolls of film to be developed and paid $219 for processing.

A. Write a system of equations to describe the situation.

B. Find the number of rolls of 24-exposure and the number of 36-exposure film that were processed using either elimination or substitution. Make sure to show your work for full credit.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
X=number of 24-exposure rolls; Y=number of 36 exposure rolls
SECTION A: System of Equations
X+Y=22
$9.00X+$12.00Y=$219
SECTION B: Solution
METHOD 1: SUBSTITUTION
Solve the first equation for X
X+Y=22 Subtract Y from each side
X=22-Y Now substitute for X in the second equation.
$9.00X+$12.00Y=$219
$9.00(22-Y)+$12.00Y=$219
$198-$9.00Y+$12.00Y=$219
$198+$3.00Y=$219 Subtract $198 from each side.
$3.00Y=$21 Divide each side by $3.00
Y=7 ANSWER 1:The number of 36-exposure rolls is 7.
Back solve in one of the equations to find X (First equation is easiest)
X+Y=22
X+7=22 Subtract 7 from each side.
X=15 ANSWER 2: There were 15 rolls of 24-exposure film.
CHECK
It is best to use the equation you did not use to back solve, so use equation 2
$9.00(X)+$12.00(Y)=$219
$9.00(15)+$12.00(7)=$219
$135+$84=$219
$219=$219
METHOD 2: ELIMINATION
X+Y=22
$9.00(X)+$12.00(Y)=$219 Multiply first equation by $9.00
$9.00(X)+$9.00(Y)=$198 Subtract this from second equation to eliminate X.
$3.00(Y)=$21 Divide each side by $3.00
Y=7 ANSWER 1: The number of 36-exposure rolls is 7.
From this point, the same as above.

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