9) Ashley is an automotive engineer. Her team designed a tractor- trailer engine that can go 4.27 km on 1 L of fuel. About how many litres of fuel would the engine need for a $$ 675-\mathrm{km} $$ trip?

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To find out how many liters of fuel the engine would need for a 675-km trip, we can use the given information that the engine can go 4.27 km on 1 L of fuel.

Let's denote the number of liters of fuel needed for the 675-km trip as $$ x $$ liters.

Given that the engine can go 4.27 km on 1 L of fuel, we can set up a proportion to find the number of liters of fuel needed for the 675-km trip:

$$
\frac{4.27 \, \text{km}}{1 \, \text{L}} = \frac{675 \, \text{km}}{x \, \text{L}}
$$

Now, we can solve for $$ x $$ to find the number of liters of fuel needed for the 675-km trip.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4.27=\frac{675}{x}$$
- step1: Find the domain:
  $$4.27=\frac{675}{x},x\neq 0$$
- step2: Swap the sides:
  $$\frac{675}{x}=4.27$$
- step3: Convert the expressions:
  $$\frac{675}{x}=\frac{427}{100}$$
- step4: Rewrite the expression:
  $$x=\frac{675\times 100}{427}$$
- step5: Divide the terms:
  $$x=\frac{67500}{427}$$
- step6: Check if the solution is in the defined range:
  $$x=\frac{67500}{427},x\neq 0$$
- step7: Find the intersection:
  $$x=\frac{67500}{427}$$
The number of liters of fuel needed for a 675-km trip is approximately $$ \frac{67500}{427} $$ liters.

Therefore, the engine would need approximately 158 liters of fuel for a 675-km trip.
The engine would need approximately 158 liters of fuel for a 675-km trip.

9) Ashley is an automotive engineer. Her team designed a tractor- trailer engine that can go 4.27 km on 1 L of fuel. About how many litres of fuel would the engine need for a \( 675-\mathrm{km} \) trip?

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