1. **Stating the problem:** Given the ratio 5:10:20, if the term corresponding to 5 is multiplied by $x$ where $x$ is 7, 8, or 9, find the value of the term corresponding to 20 multiplied by the same $x$. 2. **Understanding ratios:** A ratio compares quantities and is expressed as terms separated by colons, e.g., 5:10:20. When multiplying a term by a factor $x$, all terms scale proportionally. 3. **Applying the multiplication:** If the first term is $5x$ and $x$ is 7, 8, or 9, then the third term is $20x$. 4. **Calculating $20x$ for each $x$:** - For $x=7$, $20x = 20 \times 7 = 140$ - For $x=8$, $20x = 20 \times 8 = 160$ - For $x=9$, $20x = 20 \times 9 = 180$ 5. **Summary:** When the first term is multiplied by $x$, the third term is $20x$. For $x=7,8,9$, the third term values are 140, 160, and 180 respectively. --- **Additional notes on ratios:** - Ratios should be expressed without decimals; multiply terms by a common factor to clear decimals. - Terms must be in the same units before forming ratios. - Ratios can be simplified by dividing by the greatest common divisor. **Final answer:** $$20x = \begin{cases} 140 & \text{if } x=7 \\ 160 & \text{if } x=8 \\ 180 & \text{if } x=9 \end{cases}$$