Proportional Vs Non Proportional Worksheet PDF | airSlate SignNow - Free Printable

It looks like you've uploaded a worksheet with several math problems related to proportional and non-proportional relationships. Since I can't view images directly, I'll need you to provide the text or details of the specific problem you'd like me to solve.

However, based on the visible content in your description, here are the types of problems included:

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Problem 4 (Example):

> Use a table to solve. Then explain your reasoning.
>
> 4. For every 100 customers, 35 buy a CD. If there are 200 customers, how many CDs will be sold?

#### ✔ Solution:
We are told that for every 100 customers, 35 CDs are sold. This is a proportional relationship because the ratio stays constant.

Let’s set up a proportion:

$$
\frac{35 \text{ CDs}}{100 \text{ customers}} = \frac{x \text{ CDs}}{200 \text{ customers}}
$$

Cross-multiply:

$$
35 \times 200 = 100x \\
7000 = 100x \\
x = 70
$$

✔ So, 70 CDs will be sold when there are 200 customers.

#### 🔍 Explanation:
The relationship is proportional because the number of CDs sold increases at a constant rate relative to the number of customers. Doubling the number of customers doubles the number of CDs sold.

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Problem 5:

> Determine whether the relationship between two quantities shown in the table is proportional by graphing on the coordinate plane. Explain your reasoning.

| Number of Hours | Distance (miles) |
|-----------------|------------------|
| 1 | 40 |
| 2 | 80 |
| 3 | 120 |
| 4 | 160 |

#### ✔ Solution:
This is a proportional relationship.

Let’s check the ratio of distance to time:

- 40 / 1 = 40
- 80 / 2 = 40
- 120 / 3 = 40
- 160 / 4 = 40

All ratios are equal → constant rate → proportional.

If we were to graph this, it would be a straight line passing through the origin (0,0), which confirms proportionality.

✔ Answer: Yes, the relationship is proportional because the ratio is constant and the graph would pass through the origin.

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Problem 6:

| Weight (pounds) | Cost ($) |
|-----------------|----------|
| 1 | 1.50 |
| 2 | 3.00 |
| 3 | 4.50 |
| 4 | 6.00 |

#### ✔ Solution:
Check the cost per pound:

- $1.50 / 1 = $1.50
- $3.00 / 2 = $1.50
- $4.50 / 3 = $1.50
- $6.00 / 4 = $1.50

Constant unit rate → proportional

Graphing this would give a straight line through the origin.

✔ Answer: Yes, proportional.

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Problem 7:

> An auto repair shop charges $50 for a tune-up and $35 per hour for labor. Is the total cost proportional to the number of hours? Explain.

#### ✔ Solution:
Total cost = $50 + $35 × (number of hours)

This is not proportional because of the fixed fee ($50). Even if no hours are worked, the cost is $50.

In a proportional relationship, when one quantity is zero, the other must also be zero.

Here, when hours = 0, cost = $50 ≠ 0 → not proportional

✘ Answer: No, because there's a fixed charge regardless of time.

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Problem 8:

> A school has 120 students and 10 teachers. Is the number of students proportional to the number of teachers?

#### ✔ Solution:
Ratio = 120 / 10 = 12 students per teacher

But unless we know that this ratio holds for all class sizes, we cannot assume proportionality.

However, if we assume this ratio is consistent across different numbers of teachers and students, then yes — but only if the ratio remains constant.

But typically, schools don’t scale perfectly linearly due to constraints.

But mathematically, if the ratio is constant, it's proportional.

So assuming the ratio is always 12:1, then:

✔ Yes, it's proportional if the student-to-teacher ratio is constant.

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Problem 9:

> Myles earned $40 for mowing lawns. He earned $5 per hour. How many hours did he work?

#### ✔ Solution:
$$
\text{Hours} = \frac{\text{Total Earnings}}{\text{Rate per Hour}} = \frac{40}{5} = 8 \text{ hours}
$$

✔ Answer: 8 hours

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Problem 10:

> The table shows the number of cookies baked and the amount of sugar used.

| Cookies | Sugar (cups) |
|--------|--------------|
| 12 | 2 |
| 24 | 4 |
| 36 | 6 |
| 48 | 8 |

Is this proportional?

Check ratio:
- 2/12 = 1/6
- 4/24 = 1/6
- 6/36 = 1/6
- 8/48 = 1/6

✔ Constant ratio → proportional

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Let me know which specific problem you want explained in detail, or if you'd like help with graphing any of these!