The sum of two consecutive numbers is 41. What are the numbers?
Understand the Problem
The question is asking us to find two consecutive integers whose sum equals 41. We will define the first consecutive number as 'x' and the second as 'x + 1', and then set up the equation x + (x + 1) = 41 to solve for x.
Answer
20 and 21
Answer for screen readers
The two consecutive integers are 20 and 21.
Steps to Solve
- Set up the equation
We start with the equation based on the problem statement. Since we defined the first integer as $x$ and the second as $x + 1$, we write:
$$ x + (x + 1) = 41 $$
- Combine like terms
Next, we simplify the left side of the equation by combining like terms. This gives us:
$$ 2x + 1 = 41 $$
- Isolate the variable
We need to isolate $x$. First, subtract 1 from both sides of the equation:
$$ 2x = 41 - 1 $$
Which simplifies to:
$$ 2x = 40 $$
- Solve for x
Now, divide both sides by 2 to solve for $x$:
$$ x = \frac{40}{2} $$
This simplifies to:
$$ x = 20 $$
- Find the consecutive integers
Now that we have $x$, we can find the consecutive integers. The first integer is $x = 20$ and the second is $x + 1 = 21$.
The two consecutive integers are 20 and 21.
More Information
Consecutive integers are integers that follow one after another without any gaps. In this case, 20 and 21 are consecutive because they differ by 1. Their sum, 20 + 21, equals 41, confirming the solution.
Tips
- Assuming consecutive integers are the same. Remember that consecutive integers differ by 1.
- Forgetting to combine like terms correctly, which can lead to incorrect equations.
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