To determine the original width of the photograph, let's follow a clear step-by-step solution using the provided information about the scale factor and the reduced width.
1. Identify the Reduced Width and Scale Factor:
- The reduced width of the photograph is given as [tex]\( 15.6 \)[/tex] cm.
- The scale factor is given as [tex]\( 3:2 \)[/tex], which translates to the new width being [tex]\( \frac{3}{2} \)[/tex] times the original width.
2. Understanding the Scale Factor:
- When we reduce the size of the photograph, we actually multiply the original width by [tex]\(\frac{2}{3}\)[/tex] to get the new width.
- Mathematically, this can be written as:
[tex]\[
\text{new width} = \text{original width} \times \frac{2}{3}
\][/tex]
3. Form the Equation and Solve for the Original Width:
- Let the original width be [tex]\( x \)[/tex] cm.
- According to the scale factor ratio, the reduced width (new width) is given by:
[tex]\[
15.6 = x \times \frac{2}{3}
\][/tex]
- To find [tex]\( x \)[/tex], we solve this equation by isolating [tex]\( x \)[/tex]. Multiply both sides by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = 15.6 \times \frac{3}{2}
\][/tex]
4. Calculate the Original Width:
- Perform the multiplication step:
[tex]\[
x = 15.6 \times 1.5
\][/tex]
- Calculate the result:
[tex]\[
x = 23.4
\][/tex]
Based on this calculation, among the provided options, none of them are correct as the correct answer should have been 23.4 cm. However, if you're explicitly asking to choose among the given options, unfortunately, none exactly match the precise solution, but the result from the accurate calculation indicates the correct width of the original photograph.
