Answer:
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
Step-by-step explanation:
Let the price of popcorn be x
Let the price of drink be y.
price of 12 bags of popcorn will be 12x
price of 2 drinks will be 2y
it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."
thus
12x + 2y = 77.50
dividing LHS and RHS by 2 we have
12x/2 + 2y/2 = 77.50/2
=> 6x + y = 38.75 _________(1)
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price of 3 bags of popcorn will be 3x
price of 6 drinks will be 6y
it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."
thus
3x + 6y = 51.00
dividing LHS and RHS by 3 we have
3x/3 + 6y/3 = 51/3
=> x + 2y = 17 _____________(2)
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Thus we have two equation
6x + y = 38.75 _________(1)
x + 2y = 17
=> x = 17 - 2y
putting this value of x in equation 1 we have
6( 17 - 2y) + y = 38.75
=> 102 - 12y + y = 38.75
=> 102 - 11y = 38.75
=> -11y = 38.75 -102
=> -11y = -63.25
=> y = -63.25/-11 = 5.75
as we have x = 17 - 2y
using 5.75 in place of y
x = 17 - 2(5.75 )
=> x = 17 - 11.5
=> x = 5.5
Thus, system of equations are
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
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