Math Problem Statement

The ages of Edna, Ellie, and Elsa are consecutive integers. The sum of their ages is 108. What are their ages?

Solution

We are given that Edna, Ellie, and Elsa are consecutive integers, and their ages sum to 108. To solve for their ages, we can set up the following equations:

Let the ages of Edna, Ellie, and Elsa be:

  • Edna's age: xx
  • Ellie's age: x+1x + 1
  • Elsa's age: x+2x + 2

The sum of their ages is 108, so: x+(x+1)+(x+2)=108x + (x + 1) + (x + 2) = 108

Simplifying the equation: 3x+3=1083x + 3 = 108

Subtract 3 from both sides: 3x=1053x = 105

Now, divide by 3: x=35x = 35

So, Edna's age is 35, Ellie's age is 36, and Elsa's age is 37.

Thus, their ages are:

  • Edna: 35 years
  • Ellie: 36 years
  • Elsa: 37 years

Would you like any further details or clarifications?

Here are 5 related questions for practice:

  1. What would their ages be if the sum was 111?
  2. How would the solution change if they were consecutive even integers?
  3. What if their ages summed to 120 instead of 108?
  4. If the sum of their ages was 96, what would their ages be?
  5. How would the solution change if there were 4 people instead of 3?

Tip: When solving word problems, it often helps to assign variables to unknown quantities and create an equation based on the given relationships.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

x + (x + 1) + (x + 2) = 108

Theorems

Basic properties of consecutive integers

Suitable Grade Level

Grades 6-8