Question

You are buying sodas for a friends birthday party . You buy 50 packs . Cherry which costs $4.50 per pack, and vanilla which cots $5.00 per pack . In total you spent $238.50 on soda . Write the system of equations for this scenario.

Answer 1

Number of packs of Cherry soda: C

Number of packs of Vanilla soda: V

You buy 50 packs:

`C+V=50`

Cherry soda cost $4.50 per pack and Vanilla soda $5.00 per pack. In total you spent $238.50 on soda:

`4.50C+5.00V=238.50`

Then, the system of equations for the given scenario is:

`\begin{gathered} C+V=50 \\ 4.50C+5.00V=238.50 \end{gathered}`

To solve the system of equations:

1. Solve one of the variables in the first equation:

`C=50-V`

2. Substitute the C in the second equation by the value of C you get in step 1:

`4.50(50-V)+5.00V=238.50`

3. Solve V:

`\begin{gathered} 225-4.50V+5.00V=238.50 \\ 225+0.5V=238.50 \\ 0.5V=238.50-225 \\ 0.5V=13.5 \\ V=(13.5)/(0.5) \\ \\ V=27 \end{gathered}`

4. Use the value of V you get in step 3 and solve C:

`\begin{gathered} C=50-V \\ C=50-27 \\ C=23 \end{gathered}`

Then, you bought 23 packs of Cherry soda and 27 packs of Vanilla soda