No given situations can be represented by the proportion 1/2 = 1/4
Solution:
Given, we have to find which situations can be represented by the proportion [tex]\frac{1}{2} = \frac{1}{4}[/tex]
Let us check option by option.
Option 1:
If 8 people can wash a car in 1/4 hour, then 4 people can wash the same car in 1/2 hour.
Here the proportionality is obtained as:
[tex]\frac{8}{\frac{1}{4}}=\frac{4}{\frac{1}{2}}[/tex]
[tex]\begin{array}{l}{8 \times 4=4 \times 2} \\\\ {32=8} \\\\ {4=1 \rightarrow \text { wrong }}\end{array}[/tex]
Option 2:
If 8 people can eat 1/2 of a watermelon, then 4 people can eat 1/4 of the watermelon.
Proportionality is given as:
[tex]\begin{array}{l}{\frac{8}{2}=\frac{4}{\frac{1}{4}}} \\\\ {\rightarrow 8 \times 2=4 \times 4} \\\\ {\rightarrow 8=8 \rightarrow 1=1 \rightarrow \text { wrong }}\end{array}[/tex]
Option 3:
If 1/2 pound of steak costs $8, then 1/4 pound of steak costs $4.
[tex]\begin{array}{l}{\frac{\frac{1}{2}}{8}=\frac{\frac{1}{4}}{4}} \\\\ {\rightarrow \frac{1}{2} \times 4=8 \times \frac{1}{4}} \\\\ {\rightarrow \frac{1}{2}=2 \times \frac{1}{4}} \\\\ {\rightarrow \frac{1}{2}=\frac{1}{2}} \\\\ {\rightarrow 1=1 \rightarrow \text { Wrong }}\end{array}[/tex]
Option 4:
If 1/2 a pot holds 4 fluid Ounces of water, then 1/4 of the pot holds 8 fluid ounces
[tex]\begin{array}{l}{\frac{\frac{1}{2}}{4}=\frac{\frac{1}{4}}{8}} \\\\ {\rightarrow \frac{1}{2} \times 8=4 \times \frac{1}{4}} \\\\ {\rightarrow 4=1 \rightarrow \text { wrong }}\end{array}[/tex]
Hence, no given situation represents the proportion [tex]\frac{1}{2} = \frac{1}{4}[/tex]
