Question

9. At a movie theater, Ms. Torres purchased two boxes of popcorn and three soft drinks for $6.05. Mr. Russo purchased three boxes of popcorn and five soft drinks for $9.50. Assuming no tax, find the cost of a box of popcorn.solve for x and y

Answer 1

Let x and y represent the cost of one box of popcorn and one soft drink respectively.

Given;

Ms. Torres purchased two boxes of popcorn and three soft drinks for $6.05.

`2x+3y=6.05\text{ -----1}`

Also, Mr. Russo purchased three boxes of popcorn and five soft drinks for $9.50.

`3x+5y=9.50\text{ ------2}`

From the question we have generated a system of simultaneos equation.

we now need to solve the simultaneous equation to get the value of x and y.

Let's solve by elimination.

Firstly multiply equation 1 through by 3 and equation 2 by 2.

This is to have equal coefficient of x for the two equations, to make elimination possible.

`\begin{gathered} 2x+3y=6.05\text{ -----1 }*3 \\ 6x+9y=18.15\text{ ------3} \\ \\ 3x+5y=9.50\text{ ------2 }*2 \\ 6x+10y=19.00---------4\text{ } \end{gathered}`

Now we have equation 3 and 4.

Let us subtract equation 3 from 4.

`\begin{gathered} 6x+10y-6x-9y=19.00-18.15 \\ 6x-6x+10y-9y=0.85 \\ y=0.85 \end{gathered}`

We can now substitute the value of y into equation1 to get x