The sum of two consecutive odd integers is 24. Which equation can be used to find the first integer n?
F. n + 1=24
G. n + 2=24
H. 2n + 1=24
I. 2n + 2=24
To solve this problem, let's represent the first odd integer as n. Since the next odd integer is consecutive to the first one, it can be represented as n + 2.
Given that the sum of the two consecutive odd integers is 24, we can set up the equation:
n + (n + 2) = 24
Combining like terms, we have:
2n + 2 = 24
Therefore, the correct equation to find the first integer n is I. 2n + 2 = 24.
To solve this problem, let's break it down step by step:
Step 1: Understand the problem.
We are looking for two consecutive odd integers whose sum is 24.
Step 2: Assign variables.
Let's assume the first odd integer is "n". Since we are looking for consecutive odd integers, the second odd integer would be "n + 2".
Step 3: Write the equation.
The sum of two numbers is found by adding them together. Therefore, the equation would be n + (n + 2) = 24.
Step 4: Simplify the equation.
Combine like terms: 2n + 2 = 24.
Now, let's compare this equation to the answer choices:
F. n + 1 = 24: This equation is not correct because it only accounts for one odd integer, while we are looking for the sum of two consecutive odd integers.
G. n + 2 = 24: This equation is also incorrect because it assumes that the second odd integer is directly equal to 24, rather than accounting for the sum of the two consecutive odd integers.
H. 2n + 1 = 24: This equation is not correct because it doesn't account for the fact that we are looking for two consecutive odd integers, with a difference of 2 between them.
I. 2n + 2 = 24: This equation matches the one we derived in step 3, so it is the correct equation. Therefore, the answer is I.
1st odd integer ---- n
next odd integer --- n+2
n + n+2 = 24
2n+2 = 24