Let's break down the two parts of the question step-by-step:
### Part 1: Weight on Jupiter
The problem states that the weight ratio of an object on Jupiter compared to Earth is [tex]\( \frac{8}{3} \)[/tex]. This means an object will weigh [tex]\(\frac{8}{3}\)[/tex] times more on Jupiter than it does on Earth.
1. Given Data:
- Weight of the person on Earth [tex]\( = 100 \)[/tex] pounds
- Weight ratio (Earth to Jupiter) [tex]\( = \frac{8}{3} \)[/tex]
2. Calculating the Weight on Jupiter:
- To find the weight on Jupiter, multiply the Earth weight by the ratio:
[tex]\[
\text{Weight on Jupiter} = 100 \times \frac{8}{3}
\][/tex]
- Performing the multiplication:
[tex]\[
\text{Weight on Jupiter} = 100 \times \frac{8}{3} = 266.67 \text{ pounds}
\][/tex]
So, a person who weighs 100 pounds on Earth would weigh approximately [tex]\(266.67\)[/tex] pounds on Jupiter.
### Part 2: Amount of Paint Needed
The problem states that 1 gallon of paint covers 450 square feet. We need to determine how many gallons are required to cover a room with 675 square feet of wall surface.
1. Given Data:
- Paint coverage per gallon [tex]\( = 450 \)[/tex] square feet
- Wall surface area to paint [tex]\( = 675 \)[/tex] square feet
2. Calculating the Number of Gallons Needed:
- To find the number of gallons needed, divide the total wall surface area by the coverage per gallon:
[tex]\[
\text{Gallons needed} = \frac{675}{450}
\][/tex]
- Performing the division:
[tex]\[
\text{Gallons needed} = \frac{675}{450} = 1.5 \text{ gallons}
\][/tex]
Therefore, you would need [tex]\(1.5\)[/tex] gallons of paint to cover a room with [tex]\(675\)[/tex] square feet of wall surface.
### Summary:
1. A 100-pound person would weigh [tex]\(266.67\)[/tex] pounds on Jupiter.
2. To paint a room with [tex]\(675\)[/tex] square feet of wall surface, [tex]\(1.5\)[/tex] gallons of paint are needed.
