To find out how much oil Randi will need for 8 gallons of gas, we can use the ratio given in the problem.
The ratio of gas to oil is 5 gallons of gas for every 2 gallons of oil. This can be expressed as:
\[ \frac{5 \text{ gallons of gas}}{2 \text{ gallons of oil}} = \frac{8 \text{ gallons of gas}}{x \text{ gallons of oil}} \]
Where \( x \) is the amount of oil needed for 8 gallons of gas.
To solve for \( x \), we can set up a proportion:
\[ \frac{5}{2} = \frac{8}{x} \]
Cross-multiplying gives us:
\[ 5x = 2 \times 8 \]
Calculating the right side:
\[ 5x = 16 \]
Now, divide both sides by 5 to solve for \( x \):
\[ x = \frac{16}{5} \]
Calculating \( \frac{16}{5} \):
\[ x = 3.2 \]
Thus, Randi will need 3.2 gallons of oil for 8 gallons of gas.