Answer:
The cost of one drink is $2.5 and the cost of one bag of popcorn is $8.25
Step-by-step explanation:
Consider the provided information.
Let price of one drink is x and the price of one bag of popcorn is y.
Adam spends a total of $62.75 on 2 drinks and 7 bags of popcorn.
[tex]2x+7y=62.75[/tex]
[tex]2x=62.75-7y[/tex]......(1)
Ian spends a total of $43.00 on 4 drinks and 4 bags of popcorn.
[tex]4x+4y=43.00[/tex]
Now use substitute the value of 2x in above equation.
[tex]2(62.75-7y)+4y=43.00[/tex]
[tex]125.5-14y+4y=43.00[/tex]
[tex]-10y=43.00-125.5[/tex]
[tex]10y=82.5[/tex]
[tex]y=8.25[/tex]
Hence the value of y is $8.25
Now find the value of x as shown:
[tex]2x=62.75-7(8.25)[/tex]
[tex]2x=5[/tex]
[tex]x=2.5[/tex]
Hence, the cost of one drink is $2.5 and the cost of one bag of popcorn is $8.25
