Question

The length of a cell phone is 1, point, 41.4 inches and the width is 4, point, 24.2 inches. the company making the cell phone wants to make a new version whose length will be 1, point, 7, 51.75 inches. assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?

Answer 1

To find the width of a new cell phone that is proportional to the old cell phone, set up a proportion using the lengths and widths of the old and new phones. Solve for the unknown width to find that the width of the new phone will be approximately 86.75 inches.

Step-by-step explanation:

The original size of the cell phone has a length of 14.4 inches and a width of 24.2 inches. To find the width of the new version of the phone that has a length of 51.75 inches, we use the concept of proportional relationships. Since the new phone has to be proportional to the old phone, the ratio of the length to width of the old phone should be equal to the ratio of the length to width of the new phone.

Let's denote the unknown width of the new phone as w. We can set up a proportion comparing the old dimensions to the new dimensions:

(Old Length)/(Old Width) = (New Length)/(New Width)
(14.4 inches)/(24.2 inches) = (51.75 inches)/w

Now, we just need to solve for w:

(14.4/24.2) = (51.75/w)
14.4 * w = 24.2 * 51.75
w = (24.2 * 51.75) / 14.4
w ≈ 86.75 inches

The width of the new phone will be approximately 86.75 inches if the original and new phones are to be proportional in their dimensions.