Questions: The numbers on two consecutively numbered gym lockers have a sum of 131. What are the locker numbers? The locker numbers are 65, 66

Transcript text: The numbers on two consecutively numbered gym lockers have a sum of 131 . What are the locker numbers? The locker numbers are $\square$ (Use a comma to separate answers.)

Solution

Solution Steps

Step 1: Define the variables

Let the first locker number be $ x $. Since the lockers are consecutively numbered, the next locker number will be $ x + 1 $.

Step 2: Set up the equation

The sum of the two locker numbers is 131. Therefore, the equation is: \[ x + (x + 1) = 131 \]

Step 3: Simplify and solve the equation

Combine like terms: \[ 2x + 1 = 131 \] Subtract 1 from both sides: \[ 2x = 130 \] Divide both sides by 2: \[ x = 65 \] The next locker number is: \[ x + 1 = 66 \]

Step 4: Write the solution

The locker numbers are $ 65, 66 $.