Question

4. ** North Star's ITS club sold bags of candy and cookies to raise money for the spring musical. Bags of candy cost $6.50 and bags of cookies cost $2.00, and sales equaled $46.00 in total. There were 6 more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by ITS.

Answer 1

To solve this, it is necessary to use a system of equations

Take x as the number of bags of candy and y as the number of bags of cookies.

You know that there were 6 more bags of cookies than candy sold it means:

`y-x=6`

You also know that the sales equaled $46.00 and the unit cost of each product, the equation that represents the sales is:

`6.50x+2.00y=46.00`

Solve the system of equations:

`\begin{gathered} y-x=6 \\ 6.5x+2y=46 \end{gathered}`
`\begin{gathered} y=x+6 \\ y=(46-6.5x)/(2) \\ x+6=(46-6.5x)/(2) \\ 2x+12=46-6.5x \\ 2x+6.5x=46-12 \\ 8.5x=34 \\ x=4 \end{gathered}`

Using this value of x, find the value of y:

`\begin{gathered} y-x=6 \\ y=x+6 \\ y=4+6 \\ y=10 \end{gathered}`

The solution is x=4 and y=10, which means that there were sold 4 bags of candy and 10 bags of cookies