https://file.aiquickdraw.com/mathbot/file/17265147039687r67gcbo.jpg

We are given that the dimensions of the old phone are:

- Length = 1.4 inches
- Width = 4.2 inches

The company plans to make a new phone with a length of 1.75 inches. We need to find the width of the new phone, assuming the proportions between the length and width remain the same.

### Step-by-Step Solution:

We know that the ratio of length to width in the old phone is proportional to the ratio in the new phone. Thus, we can set up the following proportion:

\[
\frac{\text{Old Length}}{\text{Old Width}} = \frac{\text{New Length}}{\text{New Width}}
\]

Substitute the known values:

\[
\frac{1.4}{4.2} = \frac{1.75}{\text{New Width}}
\]

Now, solve for the new width:

\[
\text{New Width} = \frac{1.75 \times 4.2}{1.4}
\]

Let me calculate this for you.The width of the new phone will be approximately **5.25 inches**.

Would you like any further details or clarification on this solution?

Here are some related questions to deepen understanding:
1. How do we know that the proportions between the phones remain constant?
2. What happens to the width if the length increases more significantly?
3. How can you determine if a proportional relationship applies to different scenarios?
4. What other dimensions might change proportionally in different geometric shapes?
5. How would we calculate the area of the phone, and how does it change?

**Tip**: Proportional relationships are useful in scaling objects while maintaining their shape, and this concept is frequently applied in design and manufacturing.

The length of a cell phone is 1.4 inches and the width is 4.2 inches. The company making the cell phone wants to make a new version whose length will be 1.75 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?

In this problem, learn how to determine the width of a new phone when its length and width are proportional to the old phone. The old phone's dimensions are 1.4 inches in length and 4.2 inches in width, while the new phone will have a length of 1.75 inches. Suitable for Grades 6-8.

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