Lesson 4 Extra Practice Proportional And Nonproportional ... - Free Printable

Let’s solve each problem one by one, using the concept of proportional relationships — where two quantities change at a constant rate relative to each other. We’ll fill in the tables and explain the reasoning.

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Problem 1: Photo Center

> *Photo Center makes copies for $0.50 per copy. In addition to the hourly charge, there is a setup fee of $12. Is the number of copies you request proportional to the total cost?*

Answer: NO, it is NOT proportional.

#### Why?
A relationship is proportional if:
- It passes through the origin (0,0) — meaning when input is 0, output is 0.
- The ratio between the two quantities is constant.

Here, even if you make 0 copies, you still pay the $12 setup fee → so total cost = $12 when copies = 0.

That means the graph does not pass through (0,0), so it’s nonproportional.

Let’s fill the table:

| Copies | Total Cost ($) |
|--------|----------------|
| 0 | 12 |
| 1 | 12 + 0.50 = 12.50 |
| 2 | 12 + 1.00 = 13.00 |
| 3 | 12 + 1.50 = 13.50 |
| 4 | 12 + 2.00 = 14.00 |

✔ Conclusion: Not proportional — because of the fixed setup fee.

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Problem 2: Mrs. Garcia’s Cakes

> *Mrs. Garcia is making cakes for the school bake sale. She needs 2 cups of sugar for every cake she makes. Is the number of cakes Mrs. Garcia makes proportional to the number of cups of sugar?*

Answer: YES, it IS proportional.

#### Why?
For every cake, she uses exactly 2 cups of sugar → constant ratio:
Cups of sugar / Number of cakes = 2 → constant!

Also, if she makes 0 cakes, she uses 0 cups of sugar → passes through (0,0).

Let’s fill the table:

| Cakes | Sugar (cups) |
|-------|--------------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

✔ Conclusion: Proportional — constant ratio and passes through origin.

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Problem 3: Local Music Store – CDs

> *At a local music store, CDs cost $11.99 including tax. Is the number of CDs purchased proportional to the cost of the CDs?*

Answer: YES, it IS proportional.

#### Why?
Each CD costs the same: $11.99 → so total cost = 11.99 × number of CDs.

If you buy 0 CDs → cost = $0 → passes through origin.

Ratio: Cost / CDs = 11.99 → constant.

Table:

| CDs | Cost ($) |
|-----|----------------|
| 0 | 0.00 |
| 1 | 11.99 |
| 2 | 23.98 |
| 3 | 35.97 |
| 4 | 47.96 |

✔ Conclusion: Proportional — constant unit price and starts at zero.

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Problem 4: Jax’s Savings Account

> *Jax has $200 in her savings account. Starting next week, she will deposit $30 in her account every week. Is the amount of money in her account proportional to the number of weeks?*

Answer: NO, it is NOT proportional.

#### Why?
She starts with $200 — even at Week 0, she has $200 → doesn’t start at zero.

Total money = 200 + 30 × weeks → this is a linear relationship, but not proportional because it has a y-intercept (starting value).

Let’s fill the table:

| Weeks | Savings ($) |
|-------|----------------|
| 0 | 200 |
| 1 | 200 + 30 = 230 |
| 2 | 200 + 60 = 260 |
| 3 | 200 + 90 = 290 |
| 4 | 200 + 120 = 320 |

✔ Conclusion: Not proportional — because of the initial $200 balance.

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## ✔ Final Summary:

| Problem | Proportional? | Reason |
|---------|---------------|--------|
| 1. Photo Copies | ✘ No | Fixed setup fee → doesn’t start at 0 |
| 2. Cakes & Sugar | ✔ Yes | Constant ratio (2 cups per cake), starts at 0 |
| 3. CDs | ✔ Yes | Constant price per CD, starts at 0 |
| 4. Savings Account | ✘ No | Starts with $200 → not zero at week 0 |

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Let me know if you’d like graphs or equations for any of these!