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. 

\[\text{ Since the amount of dust picked up by the earth and the number of days are in direct variation, we have } : \]
\[\text{ Ratio of the dust picked up by the earth in pounds = ratio of the number of days taken } \]

\[ \Rightarrow \frac{10}{45} = \frac{2 . 6 \times {10}^8}{x}\]
\[ \Rightarrow x \times 10 = 45 \times 2 . 6 \times {10}^8 \]
\[ \Rightarrow x = \frac{45 \times 2 . 6 \times {10}^8}{10}\]
\[ = \frac{117 \times {10}^8}{10}\]
\[ = 11 . 7 \times {10}^8 \]
\[\text{ Thus } , 11 . 7 \times {10}^8 \text { pounds of dust will be picked up by the earth in 45 days  } .\]