Sure, let's solve this step-by-step.
1. Convert the total width from yards to inches:
- Given:
- Total width [tex]\(= 10\)[/tex] yards
- Each portrait width [tex]\(= 45\)[/tex] inches
To convert 10 yards to inches, we need to use the conversions between yards to feet and feet to inches.
- 1 yard = 3 feet
- 1 foot = 12 inches
Therefore, the total width in inches can be calculated as:
[tex]\[
\text{Total width} = 10 \text{ yd} \times 3 \text{ ft/yd} \times 12 \text{ in/ft}
\][/tex]
This converts to:
[tex]\[
\text{Total width} = 10 \times 3 \times 12 = 360 \text{ inches}
\][/tex]
2. Calculate the number of portraits that can fit in the total width:
- Each portrait is 45 inches wide.
To find how many portraits can fit in the total width, we divide the total width by the width of one portrait:
[tex]\[
\text{Number of portraits} = \frac{\text{Total width}}{\text{Width of one portrait}} = \frac{360 \text{ in}}{45 \text{ in/portrait}}
\][/tex]
Performing the division:
[tex]\[
\text{Number of portraits} = \frac{360}{45} = 8
\][/tex]
3. Fill in the blanks for the ratios and the final answer:
First, line up the necessary ratios for converting yards to inches and then to the number of portraits:
[tex]\[
\frac{10 \text{ yd}}{1} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{1 \text{ portrait}}{45 \text{ in}} = 8 \text{ portraits}
\][/tex]
So the detailed step-by-step solution is as follows:
- Starting with 10 yards:
[tex]\[
10 \text{ yd} \rightarrow
\][/tex]
- Convert to feet:
[tex]\[
10 \text{ yd} \times 3 \text{ ft/yd} = 30 \text{ ft}
\][/tex]
- Convert to inches:
[tex]\[
30 \text{ ft} \times 12 \text{ in/ft} = 360 \text{ in}
\][/tex]
- Convert inches to the number of portraits:
[tex]\[
360 \text{ in} \times \frac{1 \text{ portrait}}{45 \text{ in}} = 8 \text{ portraits}
\][/tex]
Therefore, the artist can fit 8 portraits in the display.
