Respuesta :
Answer:
The price of a drink is $10.
Step-by-step explanation:
Given:
A total of $32.50 is spend by Angel on 3 drinks and 2 bags of popcorn.
A total of $72.50 is spend by Alexander on 6 drinks and 10 bags of popcorn.
Now, to find the price of a drink.
Let the price of one drink be [tex]x.[/tex]
And let the price of one bag of popcorn be [tex]y.[/tex]
So, total money Angel spends:
[tex]3x+2y=32.50[/tex] .......(1)
Now, total money Alexander spends:
[tex]6x+10y=72.50[/tex] .......(2)
Now, to solve system of equations by multiplying the equation (1) by 2 and then subtracting equation (1) from equation (2):
[tex]3x+2y=32.50\times 2[/tex]
[tex]6x+4y=65[/tex]
Now, subtracting:
[tex]6x+10y-(6x+4y)=72.50-65[/tex]
[tex]6x+10y-6x-4y=72.50-65[/tex]
[tex]6y=7.5[/tex]
Dividing both sides by 6 we get:
[tex]y=\$1.25.[/tex]
The price of one bag of popcorn = $1.25.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]3x+2y=32.50\\\\3x+2(1.25)=32.50\\\\3x+2.5=32.50\\\\[/tex]
Subtracting both sides by 2.5 we get:
[tex]3x=30[/tex]
Dividing both sides by 3 we get:
[tex]x=10[/tex] .
The price of a drink = $10.
Therefore, the price of a drink is $10.
