Question

1. write an equation to represent the ages of 4 sisters, which are consecutive integers with the sum of 26.

Explanation:

Step1: Define the first integer

Let the first consecutive integer (age of the youngest sister) be \( x \).

Step2: Define the other integers

Since the ages are consecutive integers, the next three ages will be \( x + 1 \), \( x + 2 \), and \( x + 3 \) (representing the ages of the other three sisters).

Step3: Set up the sum equation

The sum of their ages is 26, so we add the four expressions for the ages and set it equal to 26: \( x+(x + 1)+(x + 2)+(x + 3)=26 \).

Step4: Simplify the left - hand side (optional for writing the equation, but helps in understanding)

Combine like terms: \( x+x + 1+x + 2+x + 3=(x+x+x+x)+(1 + 2+3)=4x+6 \). So the equation can also be written as \( 4x + 6=26 \), but the first form \( x+(x + 1)+(x + 2)+(x + 3)=26 \) is also correct.

Answer:

\( x+(x + 1)+(x + 2)+(x + 3)=26 \) (or \( 4x+6 = 26 \))