Respuesta :
Let be "r" the amount of money (in dollars) they are charging for a regular gift basket and "d" the amount of money (in dollars) they are charging for a deluxe gift basket.
Based on the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}26r+12d=1,166 \\ 19r+8d=819\end{cases}[/tex]You can solve the System of equations using the Substitution method:
1. Solve for "r" from the second equation:
[tex]\begin{gathered} 19r+8d=819 \\ 19r=819-8d \\ r=\frac{819-8d}{19} \end{gathered}[/tex]2. Substitute the new equation into the first original equation.
3. Solve for "d" in order to find its value.
Then:
[tex]\begin{gathered} 26r+12d=1,166 \\ \\ 26(\frac{819-8d}{19})+12d=1,166 \\ \\ 26(\frac{819-8d}{19})=1,166-12d \\ \\ \frac{21,294-208d}{19}=1,166-12d \\ \\ 21,294-208d=(19)(1,166-12d) \\ 21,294-208d=22,154-228d \\ -208d+228d=22,154-21,294 \\ 20d=860 \\ \\ d=\frac{860}{20} \\ \\ d=43 \end{gathered}[/tex]4. Knowing the value of "d", you can substitute it into the following equation, and then you must evaluate in order to find the value of "r":
[tex]r=\frac{819-8d}{19}[/tex]Then, this is:
[tex]\begin{gathered} r=\frac{819-8(43)}{19} \\ \\ r=\frac{819-344}{19} \\ \\ r=\frac{475}{19} \\ \\ r=25 \end{gathered}[/tex]The answer is: They are charging $25 for a regular gift basket and $43 for a deluxe gift basket.
