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Answer :
To solve this problem, we need to find out how much a person would weigh on Neptune if they weigh 150 pounds on Earth. We are given the ratio of an object's weight on Earth to its weight on Neptune, which is 5:7.
Here's how you can solve the problem step-by-step:
1. Understand the Ratio: A ratio of 5:7 implies that for every 5 units of weight on Earth, the object would weigh 7 units on Neptune.
2. Set Up the Proportion: You can set up a proportion where 5 units on Earth correspond to 7 units on Neptune. We can represent the weight on Earth as 150 pounds, and let [tex]\( x \)[/tex] be the weight on Neptune. So, the proportion is:
[tex]\[
\frac{5}{7} = \frac{150}{x}
\][/tex]
3. Solve the Proportion: To find [tex]\( x \)[/tex] (the weight on Neptune), you can cross-multiply and solve for [tex]\( x \)[/tex]:
[tex]\[
5 \times x = 7 \times 150
\][/tex]
[tex]\[
5x = 1050
\][/tex]
4. Divide to Find [tex]\( x \)[/tex]: Divide both sides by 5 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{1050}{5}
\][/tex]
[tex]\[
x = 210
\][/tex]
5. Conclusion: A person who weighs 150 pounds on Earth would weigh 210 pounds on Neptune.
Therefore, the correct answer is A. 210 pounds.
Here's how you can solve the problem step-by-step:
1. Understand the Ratio: A ratio of 5:7 implies that for every 5 units of weight on Earth, the object would weigh 7 units on Neptune.
2. Set Up the Proportion: You can set up a proportion where 5 units on Earth correspond to 7 units on Neptune. We can represent the weight on Earth as 150 pounds, and let [tex]\( x \)[/tex] be the weight on Neptune. So, the proportion is:
[tex]\[
\frac{5}{7} = \frac{150}{x}
\][/tex]
3. Solve the Proportion: To find [tex]\( x \)[/tex] (the weight on Neptune), you can cross-multiply and solve for [tex]\( x \)[/tex]:
[tex]\[
5 \times x = 7 \times 150
\][/tex]
[tex]\[
5x = 1050
\][/tex]
4. Divide to Find [tex]\( x \)[/tex]: Divide both sides by 5 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{1050}{5}
\][/tex]
[tex]\[
x = 210
\][/tex]
5. Conclusion: A person who weighs 150 pounds on Earth would weigh 210 pounds on Neptune.
Therefore, the correct answer is A. 210 pounds.
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