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Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 3 trips, and for each trip Lennox gets 300 dollars. On a single trip, a truck delivers 50 packs, and each pack contains 12 kilograms of apples. Overall, Lennox sells 4500 dollars worth of apples in a week.
How many trucks are in Lennox's fleet?

Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 33 trips, and for each trip Lennox gets 300300 dollars. On a single trip, a truck delivers 5050 packs, and each pack contains 1212 kilograms of apples. Overall, Lennox sells 45004500 dollars worth of apples in a week.\newlineHow many trucks are in Lennox's fleet?

Full solution

Q. Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 33 trips, and for each trip Lennox gets 300300 dollars. On a single trip, a truck delivers 5050 packs, and each pack contains 1212 kilograms of apples. Overall, Lennox sells 45004500 dollars worth of apples in a week.\newlineHow many trucks are in Lennox's fleet?
  1. Calculate income per trip: Calculate the total income per trip for one truck.\newlineReasoning: Each trip earns \(300\) dollars.\(\newline\)Calculation: 300300 dollars per trip.
  2. Determine total trips per week: Determine the total number of trips made by all trucks in a week.\newlineReasoning: Each truck makes 33 trips per week.\newlineCalculation: Let's denote the number of trucks as x x . Total trips = 3x 3x .
  3. Calculate total weekly income: Calculate the total weekly income from all trips.\newlineReasoning: Total income is the product of the number of trips and income per trip.\newlineCalculation: Total income = 3x×300 3x \times 300 = 900x 900x dollars.
  4. Set up equation for trucks: Set up the equation to find the number of trucks based on total weekly income.\newlineReasoning: We know the total weekly income from selling apples is 45004500 dollars.\newlineCalculation: 900x=4500 900x = 4500 .
  5. Solve for number of trucks: Solve for x x , the number of trucks.\newlineReasoning: Divide both sides of the equation by 900900 to isolate x x .\newlineCalculation: x=4500/900 x = 4500 / 900 .
  6. Final calculation error check: Final calculation error check.\newlineReasoning: Check if x=5 x = 5 satisfies the conditions given in the problem.\newlineCalculation: 900×5=4500 900 \times 5 = 4500 dollars, which matches the problem statement.

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