Answer:
The price of a drink is <u>$10</u>.
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 ![x.](https://tex.z-dn.net/?f=x.)
And let the price of one bag of popcorn be ![y.](https://tex.z-dn.net/?f=y.)
<u>So, total money Angel spends:</u>
.......(1)
<u>Now, total money Alexander spends:</u>
.......(2)
Now, to solve system of equations by multiplying the equation (1) by 2 and then subtracting equation (1) from equation (2):
![3x+2y=32.50\times 2](https://tex.z-dn.net/?f=3x%2B2y%3D32.50%5Ctimes%202)
<em>Now, subtracting:</em>
<em />
<em />
<em />
<em />
<em />
<em />
<em>Dividing both sides by 6 we get:</em>
![y=\$1.25.](https://tex.z-dn.net/?f=y%3D%5C%241.25.)
<u>The price of one bag of popcorn = $1.25.</u>
Now, substituting the value of
in equation (1):
![3x+2y=32.50\\\\3x+2(1.25)=32.50\\\\3x+2.5=32.50\\\\](https://tex.z-dn.net/?f=3x%2B2y%3D32.50%5C%5C%5C%5C3x%2B2%281.25%29%3D32.50%5C%5C%5C%5C3x%2B2.5%3D32.50%5C%5C%5C%5C)
<em>Subtracting both sides by 2.5 we get:</em>
<em />
<em />
<em>Dividing both sides by 3 we get:</em>
.
<u>The price of a drink = $10.</u>
Therefore, the price of a drink is $10.