To determine a 100-pound earthling's weight on Saturn, we need to find an appropriate proportion that relates the weights on Earth and Saturn.
Let's analyze the given options step by step:
### Option (a)
[tex]\[
\frac{15}{4} = \frac{b}{100}
\][/tex]
Here, we have the proportion relating the weight on Earth (15 pounds) to the weight on Saturn (4 pounds), and we are trying to find the weight [tex]\( b \)[/tex] on Saturn for a 100-pound earthling.
Using cross-multiplication:
[tex]\[
15 \times 100 = 4 \times b
\][/tex]
[tex]\[
1500 = 4b
\][/tex]
Solving for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{1500}{4} = 375
\][/tex]
### Option (c)
[tex]\[
\frac{4}{15} = \frac{100}{b}
\][/tex]
This is another way to set up the proportion. Here, the weights are inversely placed:
Using cross-multiplication:
[tex]\[
4 \times b = 15 \times 100
\][/tex]
[tex]\[
4b = 1500
\][/tex]
Solving for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{1500}{4} = 375
\][/tex]
We see that both options (a) and (c) result in the same weight on Saturn, which is 375 pounds.
### Option (b)
[tex]\[
\frac{15}{4} = \frac{100}{b}
\][/tex]
Using cross-multiplication:
[tex]\[
15 \times b = 4 \times 100
\][/tex]
[tex]\[
15b = 400
\][/tex]
Solving for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{400}{15} \approx 26.\overline{6}
\][/tex]
This option does not provide a consistent result compared to options (a) and (c) and is therefore incorrect.
### Option (d)
Since both (a) and (c) yield the same correct result, this option indicates that either (a) or (c) can be used.
Therefore, the best answer is:
D: either [tex]\( \frac{15}{4}=\frac{b}{100}\)[/tex] or [tex]\( \frac{4}{15}=\frac{100}{b}\)[/tex]
