To determine how much oil Randy will need for 8 gallons of gas, we start by finding the ratio of gas to oil given in the problem.
The mixture requires:
- 5 gallons of gas for every 2 gallons of oil.
This means the ratio of gas to oil can be expressed as: \[ \frac{\text{gas}}{\text{oil}} = \frac{5}{2} \]
To find the amount of oil required for 8 gallons of gas, we can set up a proportion based on the ratio given: \[ \frac{5 \text{ gallons of gas}}{2 \text{ gallons of oil}} = \frac{8 \text{ gallons of gas}}{x \text{ gallons of oil}} \]
Cross-multiplying gives us: \[ 5x = 2 \times 8 \] \[ 5x = 16 \]
Now, we solve for \(x\): \[ x = \frac{16}{5} = 3.2 \text{ gallons of oil} \]
Therefore, Randy will need 3.2 gallons of oil for 8 gallons of gas.
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