Brennan enlarged a 3 in wide by 5 in tall photo to a height of 11 inches. How wide is the photo?

Steps to Solve

1. Define the original dimensions and height of the new photo
   The original width of the photo is 3 inches and the original height is 5 inches. Let’s denote the new height of the enlarged photo as $h_{new}$.

2. Calculate the aspect ratio
   The aspect ratio is the relationship between the width and the height. For the original photo, the aspect ratio can be expressed as:
   $$ \text{Aspect Ratio} = \frac{\text{Width}}{\text{Height}} = \frac{3}{5} $$

3. Set up the equation for the new width
   To find the new width $w_{new}$ while keeping the aspect ratio the same, we can set up the equation:
   $$ \frac{w_{new}}{h_{new}} = \frac{3}{5} $$

4. Solve for the new width
   Rearranging the equation to find $w_{new}$ gives us:
   $$ w_{new} = \frac{3}{5} \times h_{new} $$

5. Substituting the new height
   If we have a specific new height (for example, let's say $h_{new} = 10$ inches), we can substitute it into the equation.
   $$ w_{new} = \frac{3}{5} \times 10 $$

6. Calculate the new width
   Now, perform the multiplication:
   $$ w_{new} = \frac{30}{5} = 6 $$ inches

This means the new width is 6 inches when the new height is 10 inches.