The sum of the numbers on two consecutive raffle tickets is 811,613. Find the numbers on the tickets.
The ticket numbers are $\square$ and $\square$.
Answer (2)
The two consecutive raffle ticket numbers are 405,806 and 405,807. We determined this by setting up an equation based on their sum and solving for the ticket numbers. The first ticket number is 405,806, and the next consecutive number is 405,807.
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Let the first ticket number be n , so the next consecutive number is n + 1 .
The sum of the two numbers is n + ( n + 1 ) = 811 , 613 .
Solve the equation 2 n + 1 = 811 , 613 for n , which gives n = 405 , 806 .
The two ticket numbers are 405 , 806 and 405 , 807 .
Explanation
Problem Analysis Let's analyze the problem. We are given that the sum of two consecutive raffle ticket numbers is 811,613. We need to find the numbers on the tickets. Let's denote the first ticket number as n . Since the ticket numbers are consecutive, the next ticket number will be n + 1 . The sum of these two numbers is given as 811,613. Therefore, we can write the equation as:
Setting up the Equation Now, let's set up the equation and solve for n :
n + ( n + 1 ) = 811 , 613
Simplifying the Equation Combine the terms with n :
2 n + 1 = 811 , 613
Isolating the Variable Subtract 1 from both sides of the equation: 2 n = 811 , 613 − 1 2 n = 811 , 612
Solving for n Divide both sides by 2 to find the value of n :
n = 2 811 , 612 n = 405 , 806
Finding the Second Ticket Number Now that we have the value of n , which is the first ticket number, we can find the second ticket number by adding 1 to n :
n + 1 = 405 , 806 + 1 n + 1 = 405 , 807
Final Answer So, the two consecutive raffle ticket numbers are 405,806 and 405,807.
Examples
Imagine you're organizing a race and need to assign consecutive bib numbers to participants. If you know the sum of two consecutive bib numbers, you can use this method to quickly determine the individual bib numbers. This is also applicable in scenarios like numbering houses on a street or assigning identification numbers in a sequence.
