Question

3 a theater is selling tickets to a play. adult tickets cost $8 each and childrens tickets cost $5 each. they collect $275 after selling x adult tickets and y childrens tickets.
what does the point (30, 7) mean in this situation?
4 priya starts with $50 in her bank account. she then deposits $20 each week for 12 weeks.
a. write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving.
b. technology required. graph your equation using graphing technology. mark the point on the graph that represents the amount after 3 weeks.
c. technology required. how many weeks does it take her to have $250 in her bank account? mark this point on the graph.

Explanation:

Step1: Analyze the ticket - selling situation

In the theater - ticket selling context, $x$ represents the number of adult tickets sold and $y$ represents the number of children's tickets sold. The point $(x,y)$ on the graph gives the number of each type of ticket sold.
For the point $(30,7)$:
The $x$ - coordinate is 30 and the $y$ - coordinate is 7. So, it means 30 adult tickets and 7 children's tickets were sold.

Step2: Analyze Priya's savings situation

Let $w$ be the number of weeks of saving and $A$ be the amount of money in her bank account.
She starts with $50$ and deposits $20$ each week. The linear - equation representing this relationship is $A = 50+20w$.

Step3: Find the amount after 3 weeks

Substitute $w = 3$ into the equation $A = 50+20w$.
$A=50 + 20\times3=50 + 60=110$. On the graph of $A = 50+20w$, the point $(3,110)$ represents the amount after 3 weeks.

Step4: Find the number of weeks to reach $250$

Set $A = 250$ in the equation $A = 50+20w$.
$250=50 + 20w$.
Subtract 50 from both sides: $250−50=20w$, so $200 = 20w$.
Divide both sides by 20: $w=\frac{200}{20}=10$. The point $(10,250)$ on the graph represents the situation when she has $250$ in her account.

Answer:

1. In the theater - ticket selling situation, the point $(30,7)$ means 30 adult tickets and 7 children's tickets were sold.
2. a. The equation is $A = 50+20w$.

b. The point representing the amount after 3 weeks is $(3,110)$.
c. It takes 10 weeks to have $250$ in her account, and the point is $(10,250)$.