Math Problem Statement

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 much does Lennox get for a single kilogram of apples? dollars per kilogram

Solution

We need to determine how much Lennox earns per kilogram of apples. Let's break it down step by step.

Step 1: Determine the total number of trips per week

Each truck makes 3 trips per week.

Step 2: Determine the total earnings per week

Lennox earns $300 per trip. The total earnings per week are given as:

4500 dollars4500 \text{ dollars}

Step 3: Determine the total number of packs delivered per week

Each trip delivers 50 packs of apples. The total number of packs per trip is:

Total packs per trip=50\text{Total packs per trip} = 50

Since each truck makes 3 trips per week, the number of packs delivered by one truck per week is:

3×50=150 packs per truck per week3 \times 50 = 150 \text{ packs per truck per week}

Step 4: Find the total kilograms of apples delivered

Each pack contains 12 kilograms of apples. So, the total kilograms of apples delivered per truck per week is:

150×12=1800 kg per truck per week150 \times 12 = 1800 \text{ kg per truck per week}

Step 5: Find how much Lennox earns per kilogram

We now divide the total earnings by the total kilograms of apples delivered:

45001800=2.5\frac{4500}{1800} = 2.5

Thus, Lennox earns $2.50 per kilogram of apples.

Final Answer:

2.50 dollars per kilogram\mathbf{2.50} \text{ dollars per kilogram}


Would you like a more detailed explanation or verification? Here are some related questions:

  1. How many kilograms of apples does each truck deliver per trip?
  2. If Lennox wanted to earn $6000 per week, how many more trips would need to be made?
  3. What would be the total earnings if the price per kilogram increased to $3?
  4. If each truck could carry 60 packs per trip instead of 50, how much would Lennox earn in a week?
  5. How many kilograms of apples does Lennox sell in a month (4 weeks)?

Tip: Always double-check unit conversions to avoid mistakes in price calculations!

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Math Problem Analysis

Mathematical Concepts

Unit Rate
Proportions
Multiplication
Division

Formulas

Total revenue per week = Total kilograms of apples per week × Price per kilogram
Total kilograms of apples per week = Total packs per week × Kilograms per pack
Total packs per week = Total trips per week × Packs per trip
Price per kilogram = Total revenue per week ÷ Total kilograms of apples per week

Theorems

Basic Proportionality Theorem (used in unit rate calculations)

Suitable Grade Level

Grades 6-8