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xeze [42]
3 years ago
8

In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

tors. Tickets cost $15 for students and $25 for adults. Identify the system of inequalities and the corresponding graph that determine whether the charity will reach its goal.

Mathematics
1 answer:
Maksim231197 [3]3 years ago
8 0

Answer:

See explanation

Step-by-step explanation:

Let x,\ x\ge 0 be the number of students and y,\ y\ge 0 be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

15x+25y\ge 3,750

2. The auditorium can accommodate up to 180 spectators, hence

x+y\le 180

3. We get the system of inequalities:

\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise \$(15\cdot 50+25\cdot 125)=\$3,875

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Lets use variables for each day

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now write two equations since you were given two different information (money and people)

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now you can cancel a variable but manipulating one of the equations. We'll use x, to cancel x you need make it zero so multiply the bottom by -6

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-6(x+y=1090)

6x+8y=7856                   now subtract downwards, with the x cancelling

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(2y/2)=(1316/2)              

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