Max is running the concession stand at the local football game. he is selling popcorn and water. each bag of popcorn costs $1.25 and each bottle of water costs $. 75. he sold a total of 108 items for a total of $105.00. he needs to report the number of bags of popcorn and bottles of water that were sold. determine how many of each item he sold. be sure to plug your solution back into the equation to verify that it is correct. having variables represent the popcorn and the water, so p for popcorn and w for i think the equation would be p + w = 108 and 1.25p + .75w = 105 but after that i get kind of

P= # of popcorn
w= # of waters

QUANTITY EQUATION
p + w= 108

COST EQUATION
$1.25p + $0.75w= $105

STEP 1:
solve for one variable in cost equation

p + w= 108
subtract w from both sides
p= 108 - w

STEP 2:
substitute p=108-w in for p in cost equation

$1.25p + $0.75w= $105
1.25(108-w) + 0.75w= 105
multiply 1.25 by all in parentheses
(1.25*108)+(1.25*-w)+0.75w= 105
135 - 1.25w + 0.75w= 105
combine like terms
135 - 0.5w= 105
subtract 135 from both sides
-0.5w= -30
divide both sides by -0.5
w= 60 water bottles

STEP 3:
substitute w=60 in either equation to find p

1.25p + $0.75w= $105
1.25p + 0.75(60)= 105
1.25p + 45= 105
subtract 45 from both sides
1.25p= 60
divide both sides by 1.25
p= 48 popcorn

CHECK:
p + w= 108
60 + 48= 108
108= 108

ANSWER: There were 60 popcorn sold and 48 waters sold.

Hope this helps! :)

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