Two families attended a baseball game. The first family bought 3 bags of popcorn and 4 souvenir cups, which totaled $40. The second family bought 8 bags of popcorn and 4 souvenir cups, which totaled $60. How much did one bag of popcorn cost?
Let P be the cost of one bag of popcorn and C be the cost of one souvenir cup. We can set up two equations based on the given information:
3P + 4C = 40
8P + 4C = 60
We can solve this system of equations using elimination. Multiplying the first equation by 2 and subtracting it from the second equation, we get:
2*(3P + 4C) = 2*40
8P + 4C - 6P - 8C = 60 - 80
2P = -20
Dividing both sides by 2, we get:
P = -10
This doesn't make sense as a negative cost, so we know there must be an error in our calculations. Let's try a different method: we can solve for C in the first equation and substitute it into the second equation:
3P + 4C = 40
4C = 40 - 3P
C = 10 - 0.75P
8P + 4C = 60
8P + 4(10 - 0.75P) = 60
8P + 40 - 3P = 60
5P = 20
Dividing both sides by 5, we get:
P = 4
Therefore, one bag of popcorn costs $4.
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To find the cost of one bag of popcorn, we can set up a system of equations. Let's assume that the cost of one bag of popcorn is "x" dollars.
For the first family:
3 bags of popcorn + 4 souvenir cups = $40
The equation can be written as:
3x + 4 * (cost of one souvenir cup) = $40
For the second family:
8 bags of popcorn + 4 souvenir cups = $60
The equation can be written as:
8x + 4 * (cost of one souvenir cup) = $60
Since both families bought the same number of souvenir cups, we can subtract the two equations to eliminate the souvenir cups variable:
(8x + 4 * (cost of one souvenir cup)) - (3x + 4 * (cost of one souvenir cup)) = $60 - $40
This simplifies to:
8x - 3x = $20
Now we can solve for x:
5x = $20
x = $20 / 5
Therefore, one bag of popcorn costs $4.