Math Problem Statement

Leah owns an apple orchard and allows customers to walk the orchard and pick their own apples.

Leah charges $30 for a bushel of self-picked apples. She knows that a typical bushel of the apples from her orchard weighs about 19 kilograms and wants to make sure she doesn’t overcharge or undercharge people, so she weighs each bushel before allowing it to be purchased.

What does the equation |19−x|=2 represent in this scenario? A.A bushel of apples that a customer purchases from Leah should be 19+2 kilograms. B.The maximum difference between 2 kilograms and the weight of a bushel of apples Leah sells should be 19 kilograms. C.If a bushel of apples weighs less than 19 kilograms, Leah grants a 2 -dollar discount. D.The maximum difference between 19 kilograms and the weight of a bushel of apples Leah sells should be 2 kilograms.

Solution

The equation 19x=2|19 - x| = 2 represents the absolute difference between 19 kilograms (the typical weight of a bushel of apples) and the actual weight of the bushel xx. Since the absolute value is equal to 2, it means that the weight of the bushel could differ by at most 2 kilograms from 19 kilograms.

Therefore, the correct interpretation is:

D. The maximum difference between 19 kilograms and the weight of a bushel of apples Leah sells should be 2 kilograms.

This means the bushel of apples can weigh either 2 kilograms more or less than 19 kilograms, i.e., it could weigh anywhere between 17 kg and 21 kg.

Would you like further details or have any questions?

Here are five related questions for you to consider:

  1. What would the weight of a bushel be if x=17x = 17?
  2. How would the cost change if Leah charges based on weight instead of per bushel?
  3. How could Leah use this equation to determine if a bushel is underweight?
  4. What is the significance of the number 19 in this context?
  5. How could Leah adjust the price if a bushel weighs more than 21 kg?

Tip: When working with absolute value equations, always remember they account for both positive and negative deviations from a given point.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Linear Equations

Formulas

|19 - x| = 2

Theorems

Absolute Value Theorem

Suitable Grade Level

Grades 7-9