Answer:
The cost of 1 popcorn is $5.75
The cost of 1 drink is $2.25
Step-by-step explanation:
Hi there!
First, let´s write the system of equations:
2p + 3d = 18.25
4p + 2d = 27.50
Now, let´s take the first equation (for example, it can be any equation) and solve it for "p":
2p + 3d = 18.25
Subtract 3d to both sides of the equation:
2p = 18.25 - 3d
divide both sides of the equation by 2:
p = (18.25 - 3d)/2
Now let´s replace p = (18.25 - 3d)/2 in the second equation and solve it for d:
4p + 2d = 27.50
4(18.25 - 3d)/2 + 2d = 27.50
2(18.25 - 3d) + 2d = 27.50
Apply distributive property:
36.5 - 6d + 2d = 27.50
subtract 36.5 to both sides of the equation:
-4d = 27.50 - 36.50
-4d = -9
divide both sides of the equation by -4:
d = -9/-4 = 2.25
The cost of 1 drink is $2.25
To calculate the price of popcorn, let´s use the equation we obtained above isolating "p":
p = (18.25 - 3d)/2
p = (18.25 - 3(2.25))/2
p = 5.75
The cost of 1 popcorn is $5.75
