Math Problem Statement

The weight of a dozen large eggs must be within 1.5 oz of 25.5 oz. Write and solve an equation to represent the maximum and minimum weight allowed per dozen large eggs. Malek scored an average of 9.5 points per game last season. This season, Malek has been 1.5 points above and below this average. Write and solve an equation to represent the fewest and the most points Malek has had this season.

Solution

Let's break down each of the two problems:

1) Weight of a dozen large eggs: We are told that the weight of a dozen large eggs must be within 1.5 ounces of 25.5 ounces. This means the maximum and minimum weight of the eggs can vary by 1.5 ounces from 25.5 ounces.

  • The minimum weight is:
    25.51.5=2425.5 - 1.5 = 24 ounces.

  • The maximum weight is:
    25.5+1.5=2725.5 + 1.5 = 27 ounces.

The equation representing the weight range can be written as: 24x2724 \leq x \leq 27 where xx represents the weight of a dozen large eggs in ounces.


2) Malek's points per game: Malek scored an average of 9.5 points per game last season. This season, Malek's points per game have fluctuated by 1.5 points above and below his average. We are tasked with representing this in an equation for the fewest and the most points Malek has scored this season.

  • The lowest possible score is:
    9.51.5=89.5 - 1.5 = 8 points per game.

  • The highest possible score is:
    9.5+1.5=119.5 + 1.5 = 11 points per game.

So, the equation to represent the points per game Malek has scored is: 8x118 \leq x \leq 11 where xx represents the number of points Malek has scored per game this season.


Would you like further details or clarifications on these problems? Here's a list of related questions:

  1. How do you interpret inequalities in word problems?
  2. What happens if the tolerance value changes in the egg problem?
  3. How do you solve for ranges when dealing with averages and variances?
  4. Can you think of other real-life scenarios where these types of equations apply?
  5. What does "solve an equation" mean when it comes to inequalities?

Tip: When dealing with word problems, always extract the key information first (such as numbers, average, and variations), then translate it into an equation.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Basic Algebra

Formulas

x ≤ 27
x ≥ 24
x ≤ 11
x ≥ 8

Theorems

Basic inequality solving

Suitable Grade Level

Grades 6-8