Absolutely! Let’s solve this step by step.
---
🎯 Problem Summary:
Joel is going to the State Fair of Texas.
-
Admission cost (fixed): $28.50
-
Each additional ride or food ticket: $3.50
- We need to create an equation, complete a table, graph it, and answer questions.
---
## ✍️
Step 1: Write an Equation
Let:
-
x = number of ride/food tickets Joel buys
-
y = total money Joel spends at the fair
The total cost is the
admission fee + (cost per ticket × number of tickets)
✔ So, the equation is:
>
y = 3.50x + 28.50
---
## 🧩
Step 2: Define Variables
In this situation:
-
The x variable represents →
the number of ride or food tickets Joel purchases
-
The y variable represents →
the total amount of money Joel spends at the fair
---
## 📊
Step 3: Complete the Table
We’ll plug each x-value into the equation
y = 3.50x + 28.50
| x (tickets) | y (total cost) = 3.50x + 28.50 |
|-------------|--------------------------------|
| 0 | 3.50(0) + 28.50 =
28.50 |
| 2 | 3.50(2) + 28.50 = 7.00 + 28.50 =
35.50 |
| 6 | 3.50(6) + 28.50 = 21.00 + 28.50 =
49.50 |
| 10 | 3.50(10) + 28.50 = 35.00 + 28.50 =
63.50 |
| 14 | 3.50(14) + 28.50 = 49.00 + 28.50 =
77.50 |
✔ Completed Table:
| x | y |
|---|-------|
| 0 | 28.50 |
| 2 | 35.50 |
| 6 | 49.50 |
|10 | 63.50 |
|14 | 77.50 |
---
## 📈
Step 4: Graph the Situation
You’ll plot points from the table on a coordinate plane:
- (0, 28.50)
- (2, 35.50)
- (6, 49.50)
- (10, 63.50)
- (14, 77.50)
👉 Since this is a
linear equation, the points will form a
straight line with slope 3.50 and y-intercept 28.50.
💡 Tip for graphing:
- Label x-axis: “Number of Tickets”
- Label y-axis: “Total Cost ($)”
- Start plotting from (0, 28.50) — that’s your y-intercept.
- Use a ruler to connect the dots in a straight line.
---
## ❓
Step 5: Is this relationship proportional or non-proportional? Why?
✔ Answer: Non-proportional
🔹
Why?
A proportional relationship must pass through the origin (0, 0), meaning if x=0, then y=0.
But here, when
x = 0 (no tickets bought),
y = $28.50 (admission fee).
So, there’s a
starting cost — it doesn’t start at zero. Therefore, it’s
non-proportional.
---
## 💰
Step 6: If Joel wants to buy 25 tickets, how much will he spend?
Use the equation:
y = 3.50x + 28.50
Plug in
x = 25:
> y = 3.50 × 25 + 28.50
> y = 87.50 + 28.50
>
y = $116.00
✔ So, Joel would spend
$116.00 in total.
---
##
✔ Final Answers Summary:
Equation:
>
y = 3.50x + 28.50
Variables:
- x = number of ride/food tickets
- y = total money spent
Table:
| x | y |
|---|-------|
| 0 | 28.50 |
| 2 | 35.50 |
| 6 | 49.50 |
|10 | 63.50 |
|14 | 77.50 |
Graph:
Straight line starting at (0, 28.50), increasing by $3.50 per ticket.
Proportional?
>
Non-proportional — because y ≠ 0 when x = 0 (there’s a fixed admission fee).
Cost for 25 tickets:
>
$116.00
---
Let me know if you’d like a sketch of the graph or help labeling axes! 😊
Parent Tip: Review the logic above to help your child master the concept of linear relations worksheet.
