To determine the weight of a person on Planet [tex]\(X\)[/tex] given their weight on Earth and the ratio of weights between Earth and Planet [tex]\(X\)[/tex], we can follow these steps:
1. Understand the given ratio: The ratio of the weight on Earth to the weight on Planet [tex]\(X\)[/tex] is [tex]\(2 : 7\)[/tex]. This means that for every 2 units of weight on Earth, the weight on Planet [tex]\(X\)[/tex] is 7 units.
2. Set up the relationship: Given that the weight on Earth is 160 pounds, let [tex]\( W_{X} \)[/tex] represent the weight on Planet [tex]\(X\)[/tex]. The relationship can be written as:
[tex]\[
\frac{weight\ on\ Earth}{weight\ on\ Planet\ X} = \frac{2}{7}
\][/tex]
[tex]\[
\frac{160}{W_{X}} = \frac{2}{7}
\][/tex]
3. Solve for [tex]\( W_{X} \)[/tex]: Rearrange the equation to solve for [tex]\( W_{X} \)[/tex]:
[tex]\[
160 \times 7 = 2 \times W_{X}
\][/tex]
[tex]\[
1120 = 2 \times W_{X}
\][/tex]
[tex]\[
W_{X} = \frac{1120}{2}
\][/tex]
[tex]\[
W_{X} = 560
\][/tex]
4. Round to the nearest whole number: In this case, the calculation results in a whole number. Therefore, the weight on Planet [tex]\(X\)[/tex] is:
[tex]\[
560\ pounds
\][/tex]
Thus, a person who weighs 160 pounds on Earth would weigh 560 pounds on Planet [tex]\(X\)[/tex].
