Respuesta :
Number of packs of Cherry soda: C
Number of packs of Vanilla soda: V
You buy 50 packs:
[tex]C+V=50[/tex]Cherry soda cost $4.50 per pack and Vanilla soda $5.00 per pack. In total you spent $238.50 on soda:
[tex]4.50C+5.00V=238.50[/tex]Then, the system of equations for the given scenario is:
[tex]\begin{gathered} C+V=50 \\ 4.50C+5.00V=238.50 \end{gathered}[/tex]To solve the system of equations:
1. Solve one of the variables in the first equation:
[tex]C=50-V[/tex]2. Substitute the C in the second equation by the value of C you get in step 1:
[tex]4.50(50-V)+5.00V=238.50[/tex]3. Solve V:
[tex]\begin{gathered} 225-4.50V+5.00V=238.50 \\ 225+0.5V=238.50 \\ 0.5V=238.50-225 \\ 0.5V=13.5 \\ V=\frac{13.5}{0.5} \\ \\ V=27 \end{gathered}[/tex]4. Use the value of V you get in step 3 and solve C:
[tex]\begin{gathered} C=50-V \\ C=50-27 \\ C=23 \end{gathered}[/tex]