A photographer at Roller Coaster City plans to decrease the size of this photo from 4 inches wide and 6 inches long. If the new photo will be 3 inches wide, what will be the length... A photographer at Roller Coaster City plans to decrease the size of this photo from 4 inches wide and 6 inches long. If the new photo will be 3 inches wide, what will be the length of the new photo?
Understand the Problem
The question asks us to determine the new length of a photo after it has been proportionally decreased in size. The original photo is 4 inches wide and 6 inches long, and the new width is 3 inches. We need to find the corresponding new length to maintain the same aspect ratio.
Answer
A. 4.5 inches
Answer for screen readers
A. 4.5 inches
Steps to Solve
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Set up a proportion We can set up a proportion relating the original width and length to the new width and length. Let $x$ be the new length. The proportion is: $$ \frac{\text{original width}}{\text{original length}} = \frac{\text{new width}}{\text{new length}} $$ $$ \frac{4}{6} = \frac{3}{x} $$
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Solve for the new length ($x$) To solve for $x$, we can cross-multiply: $$ 4 \cdot x = 6 \cdot 3 $$ $$ 4x = 18 $$ Divide both sides by 4: $$ x = \frac{18}{4} $$ $$ x = \frac{9}{2} $$ $$ x = 4.5 $$
A. 4.5 inches
More Information
The new length of the photo will be 4.5 inches. This maintains the same aspect ratio as the original photo.
Tips
A common mistake is setting up the proportion incorrectly by mixing up the width and length or not keeping the original and new values consistent. For example, using $\frac{4}{x} = \frac{3}{6}$ would lead to an incorrect answer. Another mistake would be performing the cross multiplication incorrectly, or making an arithmetic error in solving for $x$.
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