Respuesta :
Data:
Gummy bears: G
Chocolate kisses: C
G=50 ¢ a pound
C=30 ¢ a pound
97 pound mixture:
[tex]G+C=97[/tex]mixture worth € 35 (3500 ¢ ):
[tex]50G+30C=3500[/tex]To find how much of each type of candy is in the mixture you use the next system of equations:
[tex]\begin{gathered} G+C=97 \\ 50G+30C=3500 \end{gathered}[/tex]1. Solve one of the variables in one of the equations:
Solve G in the first equation:
[tex]G=97-C[/tex]2. Use the value you find in the fisr part in the other equation:
[tex]50(97-C)+30C=3500[/tex]3. Solve the variable:
- Distributive property to remove the parenthesis:
[tex]4850-50C+30C=3500[/tex]-Combine like terms:
[tex]4850-20C=3500[/tex]-Substract 4850 in both sides of the equation:
[tex]\begin{gathered} 4850-4850-20C=3500-4850 \\ \\ -20C=-1350 \end{gathered}[/tex]-Divide into -20 both sides of the equation:
[tex]\begin{gathered} \frac{-20}{-20}C=\frac{-1350}{-20} \\ \\ C=67.5 \end{gathered}[/tex]4. Use the value in part 3 to find the value of the other variable:
[tex]\begin{gathered} G=97-C \\ G=97-67.5 \\ \\ G=29.5 \end{gathered}[/tex]Then, the mixture has 29.5 pounds of gummy bears and 67.5 pounds of chocolate kisses