Respuesta :
Answer:
79 people can only be in this so we have 53 kids so 53 * 4 = 212
Step-by-step explanation:
However, there is 53 kids to find how many adults you will have to do 79 - 53 which that = 26 so 26 adults were there. so 26 * 8.50 = 221.
To fine how much money they earn you will just have to add them up so
$212 + $ 221 = $433 so they didn't really earn the amount of money they really want which is $ 460.
Answer:
NO SOLUTIONS
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }s=
Let s=
\,\,\text{the number of student tickets sold}
the number of student tickets sold
\text{Let }a=
Let a=
\,\,\text{the number of adult tickets sold}
the number of adult tickets sold
\text{\textquotedblleft at most 79 people"}\rightarrow \text{79 or fewer tickets}
“at most 79 people"→79 or fewer tickets
Use a \le≤ symbol
Therefore the total number of tickets sold, s+as+a, must be less than or equal to 79:79:
s+a\le 79
s+a≤79
\text{\textquotedblleft no less than \$460"}\rightarrow \text{\$460 or more}
“no less than $460"→$460 or more
Use a \ge≥ symbol
Each student ticket sells for $4, so ss student tickets will bring in 4s4s dollars. Each adult ticket sells for $8.50, so aa adult tickets will bring in 8.50a8.50a dollars. Therefore, the total amount of revenue 4s+8.50a4s+8.50a must be greater than or equal to \$460:$460:
4s+8.50a\ge 460
4s+8.50a≥460
\text{Plug in }\color{green}{53}\text{ for }s\text{ and solve each inequality:}
Plug in 53 for s and solve each inequality:
Josiah worked 53 student tickets
\begin{aligned}s+a\le 79\hspace{10px}\text{and}\hspace{10px}&4s+8.50a\ge 460 \\ \color{green}{53}+a\le 79\hspace{10px}\text{and}\hspace{10px}&4\left(\color{green}{53}\right)+8.50a\ge 460 \\ a\le 26\hspace{10px}\text{and}\hspace{10px}&212+8.50a\ge 460 \\ \hspace{10px}&8.50a\ge 248 \\ \hspace{10px}&a\ge 29.18 \\ \end{aligned}
s+a≤79and
53+a≤79and
a≤26and
4s+8.50a≥460
4(53)+8.50a≥460
212+8.50a≥460
8.50a≥248
a≥29.18
\text{It is not possible to have }a\le 26\text{ AND to have }a\ge 29.18\text{.}
It is not possible to have a≤26 AND to have a≥29.18.
\text{Therefore there is NO SOLUTION}
Therefore there is NO SOLUTION
