Question

In 10 days, the earth picks up 2.6 × 10⁸ pounds of dust from the atmosphere. How much dust will it pick up in 45 days?

Answer 1

Let the amount of dust picked up by the earth in 45 days be x pounds.

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{dust}\mathrm{picked}\mathrm{up}\mathrm{by}\mathrm{the}\mathrm{earth}\mathrm{and}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{are}\mathrm{in}\mathrm{direct}\mathrm{variation},\mathrm{we}\mathrm{have}: \\ \mathrm{Ratio}\mathrm{of}\mathrm{the}\mathrm{dust}\mathrm{picked}\mathrm{up}\mathrm{by}\mathrm{the}\mathrm{earth}\mathrm{in}\mathrm{pounds}=\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{taken} \\ \Rightarrow \frac{10}{45}=\frac{2.6\times {10}^8}{x} \\ \Rightarrow x\times 10=45\times 2.6\times {10}^8 \\ \Rightarrow x=\frac{45\times 2.6\times {10}^8}{10} \\ =\frac{117\times {10}^8}{10} \\ =11.7\times {10}^8 \\ \mathrm{Thus},11.7\times {10}^8\mathrm{pounds}\mathrm{of}\mathrm{dust}\mathrm{will}\mathrm{be}\mathrm{picked}\mathrm{up}\mathrm{by}\mathrm{the}\mathrm{earth}\mathrm{in}45\mathrm{days}. \end{gathered}$$