Question

Garrett and Carter went to the movies last weekend. Together they bought 2 drinks and 2 popcorns. They spent a total of $12.50. Thursday they met several other friends at the same theater. They purchased 6 drinks and 5 popcorns for a total of $33.75. What was the cost of one drink and one popcorn?

Answer 1

The cost of one drink is $2.50 and cost of one popcorn is $3.75

Step-by-step explanation

Suppose, the cost of one drink is
`x` dollar and cost of one popcorn is
`y` dollar.

Given that, total cost for 2 drinks and 2 popcorns is $12.50 and total cost for 6 drinks and 5 popcorns is $33.75

So, the system of equations will be......

`2x+2y=12.50 ..................................... (1)\\ \\ 6x+5y= 33.75 ..................................... (2)`

Multiplying equation (1) by -3 , we will get.....

`-3(2x+2y)=-3(12.50)\\ \\ -6x-6y=-37.50 ..................................... (3)`

Now, adding equation (2) and equation (3) , we will get ............

`5y-6y=33.75-37.50\\ \\ -y=-3.75\\ \\ y=3.75`

Plugging this
`y=3.75` into equation (1) ......

`2x+2(3.75)=12.50\\ \\ 2x+7.50=12.50\\ \\ 2x=12.50-7.50=5\\ \\ x=(5)/(2)=2.50`

So, the cost of one drink is $2.50 and cost of one popcorn is $3.75